**LCM :**

The smallest among the common multiples of two or more numbers is called their least common multiple ( LCM)

We can use few different methods to find least common multiple of given numbers

**(i) Prime factorization method**

**(ii) Grid or ladder method**

**(iv) Using venn diagram**

**Steps involved in prime factorization method :**

**Step 1 :**

Find the prime factors of the given numbers

**Step 2 : **

Circle the common prime factors

**Step 3 :**

Find the product of common prime factors. Multiply this product with the independent factors.

**Question ****1 :**

Find LCM of 24 and 60

**Solution :**

**Step 1 :**

Find the prime factors of the given numbers

List out the factors of 24 and 60

24 = 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

**Step 2 : **

Circle the common prime factors

**Step 3 :**

= 2 x 2 x 3 x 2 x 5 ==> 120

The product of common and independent factors is 120.

Hence LCM of 24 and 60 is 120.

**Question 2**** :**

Find least common multiple of 48, 72 and 108

**Solution :**

**Step 1 :**

Find the prime factors of the given numbers

List out the factors of 48, 72 and 108

48 = 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

108 = 2 x 2 x 3 x 3 x 3

**Step 2 : **

Circle the common prime factors

**Step 3 :**

= 2 x 2 x 3 x 2 x 3 x 2 x 3 ==> 432

The product of common and independent factors is 432.

Hence least common multiple of 48, 72 and 108 is 432.

**Steps involved in prime ladder method :**

**Step 1 :**

Put the given numbers inside the ladder.

**Step 2 :**

Take the smallest number that divide evenly into the given numbers.

**Step 3 :**

Write how many times it will divide into each below the line.

**Step 4 :**

Repeat steps 2 and 3 until there are prime numbers left.**Step 5 :**

Least common multiple is the product of all factors.

**Question 3**** :**

Find LCM of 24 and 60

**Solution :**

Here 24 and 60 are even numbers bot h are divisible by 2.

Since 2 and 5 are prime numbers, we cannot continue the process. So we have stopped.

Least common multiple = 2 x 2 x 3 x 2 x 5 = 120

**Question 4**** :**

Find Least common multiple of 48, 72 and 108

**Solution :**

Here 48,72 and 108 are even numbers. So all are divisible by 2.

Since 2 and 3 are prime numbers, we cannot continue the process. So we have stopped.

LCM = 2 x 2 x 3 x 3 x 3 x 2 x 2 x 1 x 3 = 432

"Venn diagram method for HCF and L.C.M" is the easiest way to find HCF and L.C.M of two numbers. Because, often some people find it difficult to find HCF and L.C.M. At that time they are in need of the easiest way to find HCF and L.C.M. That is nothing but the shortcut to find HCF and L.C.M.

**Steps involved in "Venn diagram method for HCF and L.C.M"**

To know "Venn diagram method for HCF and L.C.M, we have to be knowing the following steps explained.

**Step 1 :**

We have to decompose the given numbers in to prime factors.

In the example shown above, we have the two numbers 24 and 60.

24 = 2x2x2x3

60 = 2x2x3x5

**Step 2 :**

Now, we have to draw two circles as shown above. The first one is for "24" and the second one is for "60"

**Step 3 :**

In the prime factors of 24 and 60, strikeout the common factor (which is found in both 24 and 60) and write that one in common region (intersection part) of two circles.

**Step 4 :**

If we find a prime factor which is in "24" but not in "60", strikeout that one and it has to be written in the circle of "24" (not in the common region).

If we find a prime factor which is in "60" but not in "24", strike out that one and it has to be written in the circle of "60" (not in the common region).

This process has to be continued until all the prime factors of both "24" and "60 are struck out.

**Step 5 :**

Once all the prime factors of both "24" and "60" are struck out, we have to do the following works to get HCF and L.C.M.

H.C.F = Multiply the prime factors which are found in the common region (Intersection part).

Hence H.C. F of 24 and 60 = 2x2x3 = 12

L.C.M = Multiply all the prime factors which are found in the two circles (Including the prime factors in the common region)

Hence L.C.M of 24 and 60 = 2x2x2x3x5 = 120

- HCF calculator
- Venn diagram method for hcf and l.c.m
- Shortcut to find hcf and l.c.m
- How to solve hcf and l.c.m problems
- How to solve hcf and l.c.m word problems
- HCF and l.c.m worksheets
- Practical use of L.C.M
- L.C.M method for time and work
- L.C.M worksheet
- L.C.M calculator
- L.C.M and GCD worksheets

After having gone through the stuff given above, we hope that the students would have understood "Least common multiple".

Apart from the stuff given above, if you want to know more about "Least common multiple", please click here

Apart from the stuff, "Least common multiple", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**