HCF and LCM

H.C.F.  – Highest common factor

L.C.M. – Lowest Common Multiple

Fundamental Rules:

• Multiplication of both the numbers of L.C.M and H.C.F.  = Multiplication of both numbers.
• L.C.M. of Fraction = L.C.M. of Numerator/ H.C.F. of Denominator
• H.C.F. of Fraction = H.C.F.. of Numerator/ L.C.M. of Denominator

1. The L.C.M of two numbers is 112 and the H.C.F. is 4. If one number is 28, find out the other number?

(A) 16

(B) 20

(C) 32

(D) 28

2. The L.C.M. of two numbers is 280 and there H.C.F is 7. One of the number is 35 . Find the other number.

(A) 42

(B) 56

(C) 28

(D) 48

3. Find out simplest number which is divisible by 12, 15, 20, and perfect square.

(A) 400

(B) 900

(C) 64

(D) 81

4. Find the least number which when divided by 8,9,12 and 15 , leave the reminder 1

(A) 359

(B) 181

(C) 361

(D) 179

5. Find the least number which when divided by 8,12 and 16 leaves 3 as remainder in each case. But when divided by 7, leaves no remainder?

(A) 98

(B) 112

(C) 147

(D) 51

6. Find the least number divisible by 4,6,8 and 20 and it must be a perfect square.

(A) 1000

(B) 600

(C) 1800

(D) 3600

7. The greatest number that must be taken out from 999, such that the resulting number may be divisible by 10, 15, 18 is

(A) 900

(B) 909

(C) 180

(D) 819

8. The L.C.M. 2/5, 6/25, and 8/35 is : ?

(A) 12/5

(B) 2/180

(C) 24/5

(D) 24/4

9. Traffic light at one particular crossing changes after every 40 second. The traffic light at the next crossing changes after every 32 seconds. At a certain time they change together. After what time will they again change together?

(A) 60 Seconds

(B) 120 Seconds

(C) 160 seconds

(D) 20 Seconds

10. What is the smallest number which when divided by 12 leaves 10, When divided by 16 leaves 14 and When divided by 24 leaves 22 as reminder.

(A) 46

(B) 64

(C) 460

(D) 94

Ans: 1: A, 2: B, 3: B, 4: D, 5: C, 6: D, 7: B, 8: C, 9: C, 10: B