Question 1

The product of HCF and LCM of 18 and 15 is

Accepted Answer

HCF of 18 and 15 18 = 2 x 3 x 3 15 = 3 x 15 = 3 LCM of 18 and 15 = 2 x 3 x 3 x 5 = 90 ∴ Product of HCF and LCM of both numbers = 3 x 90 = 270

Question 2

The HCF of two numbers is 15 and their LCM is 225. If one of the numbers is 75, then find the another number.

Accepted Answer

Let the other number = N Product of LCM and HCF = Product of two numbers Then, N x 75 = 15 x 225 ∴ N = (15 x 225)/75 = 45

Question 3

The HCF of three numbers is 23. If they are in the ratio of 1 : 2 : 3, then find the numbers?

Accepted Answer

Let the numbers are N, 2N and 3N. Where, N = HCF Given that, N = 23 ∴ The numbers are 23, 46 and 69.

Question 4

The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to

Accepted Answer

We have, m x n = 6 x 210 = 1260 ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35

Question 5

The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF is

Accepted Answer

Let numbers are 5N and 6N. Now, HCF of these two numbers is N. We know that, LCM x HCF = Product of two numbers ⇒ 480 x N = 5N x 6N ⇒ 480N = 30N2 ⇒ N =16

Question 6

If a number is exactly divisible by 11 and 13, which of the following types the number must be?

Accepted Answer

LCM of 11 and 13 will be (11 x 13). Hence, if a number is exactly divisible by 11 x 13, then the same number must be exactly divisible by their LCM or by (11 x 13).

Question 7

The LCM of two numbers is 48. The numbers are in the ratio of 2 : 3. Find the sum of the numbers.

Accepted Answer

Let numbers are 2N and 3N. According to the question, 6N = 48 ⇒ N = 8 ( ∵ LCM = 6N ) ∴ Required sum = ( 2N + 3N ) = 5N = 5 x 8 = 40

Question 8

The Product of two whole numbers is 1500 and their HCF is 10, Find the LCM.

Accepted Answer

Given that, product of two numbers =1500 HCF = 10 According to the formula, Product of two numbers = HCF x LCM ⇒ 1500 = 10 x LCM ∴ LCM = 1500/10 =150

Question 9

The least number which should be added to 2497, so that the sum is exactly divisible by 5, 6, 4 and 3, is

Accepted Answer

LCM of 5, 6, 4 and 3 = 60 On dividing 2497 by 60, the remainder is 37. ∴ Number to be added = 60 - 37 = 23

Question 10

The least number which when divided by 12,16 and 18 leaves 5 as remainder in each case. Find the number.

Accepted Answer

Given, a = 12, b =16 , c =18, k = 5 According to the formula, Required number =(LCM of a, b and c) + k = (LCM Of 12, 16, 18) + 5 LCM of 12, 16, 18 is ∴ LCM = 2 x 2 x 3 x 4 x 3 = 144 ∴ Required number =144 + 5 = 149

Question 11

What least number must be subtracted from 1294 so that the remainder when divided by 9, 11,13 will leave in each case the same remainder 6?

Accepted Answer

The number when divided by 9, 11, 13 leaving remainder 6 = (i.c.m. of 9, 11, 13) + 6 = 1293 Required least number = 1294 - 1293 = 1.

Question 12

Find the number lying between 900 and 1000 which when divided by 38 and 57, leaves in each case a remainder 23?

Accepted Answer

The least common multiple of 38 and 57 is 114 and the multiple which is between 900 and 1000 is 912. Now, 912 + 23 i,e 935 lies between 900 and 1000 and when divided by 38 and 57 leaves in each case 23 as the remainder. Therefore, 935 is number required.

Question 13

Find the sum of three numbers which are prime to one another such that the product of the first two is 437 and that of the last two is 551?

Accepted Answer

From the question we see that the second number is a common factor of the two products and since the numbers are prime to one another. It is their . H. C. F . and is, therefore, 19. ∴ The first number = 437 / 19 = 23 and the third number = 551 / 19 = 29 Hence, the number are 23, 19 and 29 ∴ Sum = 23 + 19 + 29 = 71.

Question 14

What least number must be subtracted from 1936, so that the remainder when divided by 9, 10, 15 will leave in each case the same remainder 7?

Accepted Answer

The L.C.M of 9, 10, 15 = 90 On dividing 1936 by 90, the remainder = 46 But a part of this remainder = 7 Hence, the two numbers = 46 - 7 = 39.

Question 15

An inspector of schools wishes to distribute 84 balls and 180 bats equally among a number of boys. Find the greatest number receiving the gift in this ways?

Accepted Answer

Find the H.C.F. of 84 and 180, which is 12 and this is the required answer .

Question 16

The greatest possible length which can be used to measure exactly the lengths 7m, 3m 85cm, 12m 95 cm, is?

Accepted Answer

Required length = H.C.F of 700, 385, 1295 cm = 35 cm.

Question 17

The sum of two number is 216 and their H.C.F is 27. The numbers are?

Accepted Answer

Let the number be 27a and 27b Then, 27a + 27b = 216 or a + b = 216/27 = 8 ∴ Values of co-primes with sum 8 are (1, 7) and (3, 5) So, the number are (27 x 1 , 27 x 7) i.e. (27, 189)

Question 18

The product of two-digit numbers is 2160 and their G.C.M is 12. The numbers are?

Accepted Answer

Let the number be 12a and 12b Then 12a x 12b = 2160 or ab = 15 ∴ Values of co-primes a and b are (1, 15), (3, 5) So, the two digit number are 12 x 3 and 12 x 5 i.e. 36 and 60 .

Question 19

The H.C.F of two number is 16 and their L.CM is 160. If one of the numbers is 32, then the other number is?

Accepted Answer

Product of two numbers = LCM of two numbers x HCF of two numbers. ⇒ N x 32 = 160 x 16 ∴ N = 80

Question 20

The product of two numbers is 1600 and their H.C.F is 5. The L.C.M. of the numbers is?

Accepted Answer

Product of two numbers = LCM of two numbers x HCF of two numbers. ⇒ 1600 = LCM x 5 ∴ LCM = 320

Problems on H.C.F and L.C.M Questions