LCM / HCF

LCM

For example, to find the LCM of 6, 18, 28 list the prime factors of each number.
6: 2 x 3
18: 2 x 3 x 3
28: 2 x 2 x 7

Multiply each factor the greatest number of times it occurs in any of the numbers. 6 has one 2 and one 3; 18 has one 2 and two 3s, and 28 has two 2s and one 7.

We multiply 2 two times; 3 two times; and 7 once. This gives us 252, the smallest number that can be divided evenly by 6, 18, and 28.

HCF

For example, 6 is the greatest number that will divide into 12, 18 and 72 without a remainder.

In the illustration above 12, 18 and 72 is the group of numbers.

• When the common factor of 2 is taken into account the remaining values are 6, 9 and 36.
• With the next common factor of 3 the results become 2, 3 and 12.

Since there are no more common factors between 2, 3 and 12 the HCF would be : 2x3=6.

In other words, HCF is that number that is contained in each member of a group. The HCF is the multiple of all prime factors that 12, 18 and 72 share. This is how the HCF is determined.

Now that you know the method here is the easy part.