# LEAST COMMON MULTIPLE BY PRIME FACTORIZATION WORKSHEET

In each case, find the least common multiple of the numbers by prime factorization.

Problem 1 :

4 and 6

Problem 2 :

2 and 3

Problem 3 :

4 and 5.

Problem 4 :

3 and 6

Problem 5 :

12 and 18

Problem 6 :

24 and 60

Problem 7 :

4, 5 and 8

Problem 8 :

48, 72 and 108

Problem 9 :

4, 6, 8 and 12

Problem 10 :

2, 3, 4 and 5

Problem 11 :

2, 4, 5 and 8

Problem 12 :

3, 6, 7 and 14

4 and 6

Resolve the given numbers into their prime factors.

From the above division,

4 = 2 x 2

6 = 2 x 3

The different prime factors are 2 and 3.

The prime factor 2 appears a maximum of 2 times in the prime factorization of 4.

The prime factor 3 appears a maximum of 1 time in the prime factorization of 6.

Therefore, the least common multiple of 4 and 6 is

= 2 x 2 x 3

= 12

2 and 3

There is no common divisor for 2 and 3 other than 1. So, 2 and 3 are relatively prime.

To get least common multiple of relatively prime numbers, we have to multiply them.

Therefore, the least common multiple of 2 and 3 is

= 2 x 3

= 6

4 and 5

There is no common divisor for 4 and 5 other than 1. So, 4 and 5 are relatively prime.

To get least common multiple of relatively prime numbers, we have to multiply them.

Therefore, the least common multiple of 4 and 5 is

= 4 x 5

= 20

3 and 6

Since 3 is a prime number, we don't have to resolve it into prime factors anymore.

Resolve 6 into its prime factors.

From the above division,

6 = 2 x 3

3 is already a prime number.

3 = 3

The different prime factors are 2 and 3.

The prime factor 2 appears a maximum of 1 time in the prime factorization of 6.

The prime factor 3 appears a maximum of 1 time in the prime factorization of 6 and 3.

Therefore, the least common multiple of 3 and 6 is

= 2 x 3

= 6

12 and 18

Resolve 12 and 18 into their prime factors.

From the above division,

12 = 2 x 2 x 3

18 = 2 x 3 x 3

The different prime factors are 2 and 3.

The prime factor 2 appears a maximum of 2 times in the prime factorization of 12.

The prime factor 3 appears a maximum of 2 times in the prime factorization of 18.

Therefore, the least common multiple of 12 and 18 is

= 2 x 2 x 3 x 3

= 36

24 and 60

Resolve 24 and 60 into their prime factors.

From the above division,

24 = 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

The different prime factors are 2, 3 and 5.

The prime factor 2 appears a maximum of 3 times in the prime factorization of 24.

The prime factor 3 appears a maximum of 1 time in the prime factorization of 24 and 60.

The prime factor 5 appears a maximum of 1 time in the prime factorization of 60.

Therefore, the least common multiple of 24 and 60 is

= 2 x 2 x 2 x 3 x 5

= 120

4, 5 and 8

Since 5 is a prime number, we don't have to resolve it into prime factors anymore.

Resolve 4 and 8 into their prime factors.

From the above division,

4 = 2 x 2

8 = 2 x 2 x 2

5 is already a prime number.

5 = 5

The different prime factors are 2 and 5.

The prime factor 2 appears a maximum of 3 times in the prime factorization of 8.

The prime factor 5 appears a maximum of 1 time in the prime factorization of 5.

Therefore, the least common multiple of 4, 5 and 8 is

= 2 x 2 x 2 x 5

= 40

48, 72 and 108

Resolve 48, 72 and 108 into their prime factors.

From the above division,

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

The different prime factors are 2 and 3.

The prime factor 2 appears a maximum of 4 times in the prime factorization of 48.

The prime factor 3 appears a maximum of 3 times in the prime factorization of 108.

Therefore, the least common multiple of 48, 72 and 108

= 2 x 2 x 2 x 2 x 3 x 3 x 3

= 432

4, 6, 8 and 12

Resolve 4, 6, 8 and 12 into their prime factors.

From the above division,

4 = 2 x 2

6 = 2 x 3

8 = 2 x 2 x 2

12 = 2 x 2 x 3

The different prime factors are 2 and 3.

The prime factor 2 appears a maximum of 3 times in the prime factorization of 8.

The prime factor 3 appears a maximum of 1 time in the prime factorization of 6 and 12.

Therefore, the least common multiple of 4, 6, 8 and 12 is

= 2 x 2 x 2 x 3

= 24

2, 3, 4 and 5

There is no common divisor for all the four numbers 2, 3, 4 and 5. So, the given numbers are relatively prime.

To get least common multiple of relatively prime numbers, we have to multiply them.

Therefore, the least common multiple of 2, 3, 4 and 5 is

= 2 x 3 x 4 x 5

= 120

2, 4, 5 and 8

Since 2 and 5 are prime numbers, we don't have to resolve them into prime factors anymore.

Resolve 4 and 8 into their prime factors.

From the above division,

4 = 2 x 2

8 = 2 x 2 x 2

2 and 5 are already prime numbers.

2 = 2

5 = 5

The different prime factors are 2 and 5.

The prime factor 2 appears a maximum of 3 times in the prime factorization of 8.

The prime factor 5 appears a maximum of 1 time in the prime factorization of 5.

Therefore, the least common multiple of 2, 4, 5 and 8 is

= 2 x 2 x 2 x 5

= 40

3, 6, 7 and 14

Since 3 and 7 are prime numbers, we don't have to resolve them into prime factors anymore.

Resolve 6 and 14 into their prime factors.

From the above division,

6 = 2 x 3

14 = 2 x 7

3 and 7 are already prime numbers.

3 = 3

7 = 7

The different prime factors are 2, 3 and 7.

The prime factor 2 appears a maximum of 1 time in the prime factorization of 6 and 14.

The prime factor 3 appears a maximum of 1 time in the prime factorization of 6 and 3.

The prime factor 7 appears a maximum of 1 time in the prime factorization of 14 and 7.

Therefore, the least common multiple of 3, 6, 7 and 14 is

= 2 x 3 x 7

= 42

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