Page 3 - ln6

We can read the explanation and see below the L.C.M. of 120, 144, 160 and 180.

First we write all the numbers i.e. 120, 144, 160 and 180 in a row separating them by a dash
or comma. Then we divide by a least prime number i.e. 2 which divides all the given numbers.
Now we put the quotient i.e. 60, 72, 80 and 90 directly under the numbers in the next row.

Then again we divide by 2 and put the quotient i.e. 30, 36, 40 and 45 directly under the
numbers in the next row.

We continue the process and similarly we divide by 2 and put the quotient i.e. 15, 18, 20 and
45. Here 45 will remain as it is because we can’t divide 45 by 2. So we directly write under the
numbers in the next row.

Similarly again, we divide by 2 and put the quotient i.e. 15, 9, 10 and 45. Here 15 and 45 will
remain as it is because we can’t divide 15 and 45 by 2 and we directly write under the
numbers in the next row.

According to the explanation we continue the process and until all co-prime numbers are left
in the last row.

And at last we multiply all the prime numbers by which we have divided and the co-prime
numbers left in the last row i.e. 2 × 2 × 2 × 2 × 3 × 3 × 5 × 2 = 1440.

Therefore, the product is the least common multiple of 120, 144, 160 and 180 is 1440.

1. What is the least common multiple (L.C.M) of 3, 12 and 16 by using division method?

Solution:

Least common multiple (L.C.M) of 3, 12 and 16 = 3 × 2 × 2 × 2 × 2 = 48.

2. What is the least common multiple (L.C.M) of 12, 30 and 40by using division
method?
Solution: