HCF AND LCM WORKSHEETS 1

About HCF and LCM worksheets 1

In this HCF and LCM worksheets 1,we give the questions on HCF and LCM whose qualities  are in high standard and practicing these questions will definitely make the students to score marks in HCF and LCM.

Example Quiz 1

1. Find the HCF of 23x32x5x74, 22x35x52x76, 23x53x72

 (A) 979 (B) 980 (C) 981 (D) 982

2. Find the LCM of 22x33x5 , 23x32x52, 2x3x52

 (A) 5400 (B) 5410 (C) 5420 (D) 5430

3. Find the H.C.F of 0.63, 1.05, and 2.1

 (A) 0.21 (B) 0.22 (C) 0.23 (D) 0.24

4. Two numbers are in the ratio of 15:11. If their HCF is 13, find the numbers.

 (A) 196 and 144 (B) 196 and 143 (C) 195 and 144 (D) 195 and 143

5. The HCF of two numbers is 11 and their LCM is 693. If one of the numbers is 77, find the other.

 (A) 99 (B) 88 (C) 77 (D) 66

6. Find the L.C.M of 16, 24, 36 and 54.

 (A) 430 (B) 431 (C) 432 (D) 433

7. Find the H.C.F of 513, 1134, and 1215.

 (A) 27 (B) 28 (C) 29 (D) 30

8. Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm.

 (A) 45 cm (B) 44 cm (C) 43 cm (D) 42 cm

9. Find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.

 (A) 126 (B) 127 (C) 128 (D) 129

10. Find the largest number which divides 62, 132 and 237 leaves the same remainder in each case.

 (A) 32 (B) 33 (C) 34 (D) 35

 Question No.1 Question No.2 Question No.3 Question No.4 Question No.5 Question No.6 Question No.7 Question No.8 Question No.9 Question No.10 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} 23x32x5x74, 22x35x52x76, 23x53x72 In the above given numbers, we find 2, 5 and 7 in common. Take 2, 5 and 7 with minimum power. That is 22, 5, 72 Now, H.C.F = 22x5x72 = 980 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} 22x33x5 , 23x32x52, 2x3x52 In the above given numbers, take all prime factors with maximum power. They are, 23, 33, 52 Now, L.C.M = 23x33x52 = 5400 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} We we look in to the given numbers 0.63, 1.05, and 2.1, maximum number of digits after the decimal is 2. So, let us multiply each number by 100 to avoid decimal. When the given numbers are multiplied by100, we get 63, 105, 210 63 = 32x7 105 = 5x3x7 210 = 2x5x3x7 In the prime factors (63, 105, 210), we find 3 and 7 in common Take 3 and 7 with minimum power. They are 31 and 71 Now, H.C.F of (63, 105, 210) = 31x71 = 21 To get H.C.F of (0.63, 1.05, 2.1), divide 21 by 100. 21/100 = 0.21 Therefore, H.C.F of (0.63, 1.05, 2.1) = 0.21 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} From the given ratio, two numbers are 15x and 11x. H.C.F of 15x and 11x = x ---(1) Given : H.C.F of two numbers = 13 ---(2) From(1)& (2), we get x = 13 15x = 15(13) = 195 11x = 11(13) = 143 Hence, the two numbers are 195 and 143 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Given: One of the numbers = 77, H.C.F = 11 and L.C.M = 693 Let "x" be the other number. Product of two numbers = Product of their H.C.F and L.C.M 77x = 11X693 x = 99 Hence, the other number is 99 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Given numbers are 16, 24, 36, 54 16 = 24 24 = 23x3 36 = 22x32 54 = 2x33 In the above prime factors of (16, 24, 36, 54), take all prime factors with maximum power. They are 24 and 33 Now, L.C.M = 24x33 = 432 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Given numbers are 513, 1134, 1215 513 = 33x19 1134 = 2x34x7 1215 = 35x5 In the above prime factors of (513, 1134, 1215), we find 3 in common.So, take 3 with minimum power. That is 33 Now, H.C.F = 33 = 27 jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Required greatest possible length = H.C.F of (495, 900, 1665) 495 = 32x5x11 900 = 22x32x52 1665 = 32x5x37 In the prime factors of (495, 900, 1665), we find 3 and 5 in common. Take 3 and 5 with minimum power. They are 32 and 5 Now, H.C.F = 32x5 = 45 Hence, the required greatest possible length is 45 cm jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Required greatest number = H.C.F. of (1657 - 6) and (2037 - 5) = H.C.F. of (1651, 2032) = 127. jQuery UI Accordion - Default functionality .ui-widget-overlay,.ui-state-disabled,ui-button{background:#fff;border:1px solid #fff;color:#b9cd6d;font-weight:bold} Required Number = H.C.F of [(132-62), (237-132), and (237-62)] = H.C.F of [70, 105, 175] = 35

Quantitative Aptitude Tricks

Aptitude Test Online

jQuery UI Accordion - Default functionality
For each divisor and corresponding remainder, we have to find the difference.

35-25=10
45-35=10
55-45=10

we get the difference 10 (for all divisors and corresponding remainders)

Now we have to find the L.C.M of (35,45,55) and subtract the difference from the L.C.M.

L.C.M of (35,45,55) = 3465

Hence the required least number = 3465-10 = 3455