# HCF and LCM

H.C.F:

It is the Highest Common Factor. It is also known as "Greatest Common Factor". The largest positive integer which divides two or more integers without any remainder is called Highest Common Factor (HCF) or Greatest Common Divisor or Greatest Common Factor (GCF).

Example: What is the HCF of (24, 56).

Factors of 24 are 2 * 2 * 2 * 3.

Factors of 56 are 2 * 2 * 2 * 7.

The Common factors are 2 * 2 * 2 = 8.

The HCF of (24, 56) is 8.

L.C.M:

The least common multiple (LCM) of 2 numbers is the smallest number that they both divide evenly into. One good way to find the least common multiple of 2 numbers is to multiply both numbers by 1,2,3,4,5... and then find the first multiple that appears in both lists.

Example: The Least Common Multiple of 3 and 5 is 15, because 15 is a multiple of 3 and also a multiple of 5. Other common multiples include 30 and 45, etc, but they are not the smallest (least).

1

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

2

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is

3

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

4

Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

5

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: