LCM and its methods

LCM of two numbers is the smallest number (non zero) that is multiple of both.

When we add or subtract any fraction, we make use of the least common denominator and least common denominator is nothing but the least common multiple of more than two numbers.

LCM - least Common Multiplies actually the least possible common multiple of two or more than two numbers. We can find the least common multiple by using two methods: -

Methods for finding LCM of numbers:-
1. LCM Using Prime Factorization– In this method we find the prime multiples of all the numbers for which we need to find the Least common multiple.
We find the common factors among them and the uncommon factors. Least Common Multiple is product of common factors and product of uncommon factors.

LCM Examples- Suppose we need to find the least common multiple of 15 and 25.
We see that 15 = 3 times 5 and 25 is 5 times 5.
Now we see common factor is 5 and uncommon factors are 3 and 5.
So the least common multiple will be 3 times 5 times 5 which equal 75. Hence the least common multiple of 15 and 25 is 75.

2. Common division method- The other method of finding the least common multiple is the common division method in which we arrange the numbers together separated by commas.
We start dividing with the smallest prime number and go on dividing, till none of the numbers can be divided any further.

For example:- If we need to find LCM of 20 and 30 by common division method, we first divide both of them by 2, we get 10, 15. Then we divide again by 2, we get 5, 15. Now we divide by 3, we get 5, 5 and lastly by 5, we get 1, 1.
Now we multiply all the prime numbers by which we divided. They are 2, 2, 3, 5 which is 2 times 2 times 3 times 5 and that gives 60. Hence the least common multiple of 20 and 30 is 60.

We can try different problems for LCM Practice.
We can find the least common multiple of more than two numbers also.
This is usually helpful when we are adding and subtracting the fractions.