Question

Write all the numbers less than 100 which are common multiples of 3 and 4.

Answer 1

Hint: If we want to find the common multiples of the two given numbers under a condition, then we will find the multiples of the LCM i.e. least common multiple of those two numbers under that condition.

In this question, we are asked to find all the numbers that are less than 100 and are a common multiples of 3 and 4. The common multiples of 3 and 4 will be the multiples of their LCM i.e. least common multiple. The least common multiple of 3 and 4 is 12. So, we have to find all the multiples of 12 which are less than 100.
Let us write down the multiples of 12.
$12\times 1=12$
$12\times 2=24$
$12\times 3=36$
$12\times 4=48$
$12\times 5=60$
$12\times 6=72$
$12\times 7=84$
$12\times 8=96$
$12\times 9=108$
The last multiple of 12 which is less than 100 is 96 and $96=12\times 8$ . So, there are 8 multiples of 12 that have their value less than 100. Those multiples are 12, 24, 36, 48, 60, 72, 84 and 96.
So, we have 12, 24, 36, 48, 60, 72, 84 and 96 as the common multiples of 3 and 4 that are less than 100.

Note: If in the question, we were asked the number of common multiples of 3 and 4 that are less than 100, then we would have first found the least common multiple of 3 and 4 i.e. 12. Then to find the number of multiples of 12 which are less than 100, we would have solved the inequality