Question

What is the LCM of 30 and 33?

Answer 1

Hint: LCM is the least common multiple. For that we will find the factors of both the numbers. Then taking the common numbers in the factors once and then the remaining factors of both. Multiplication of these will give the LCM of the numbers given. This is the prime factorisation method.

Complete step by step solution:
Given the numbers are 30 and 33.
Now we will find the factors of 30 and 33.
Factors of 30 are \[30 = 2 \times 3 \times 5\]
Factors of 33 are \[33 = 3 \times 11\]
Now the common factor is 3 only.
Uncommon factors are \[2 \times 5 \times 11\]
So the LCM will be,
 \[LCM = 3 \times 2 \times 5 \times 11 = 330\]
This is the lowest common multiple of 30 and 33.
So, the correct answer is “330”.

Note: Note that, the numbers are too small to find their LCM. Like we can simply find the multiple and then take the common out of it. But here we used the method that will help even to find the LCM of two large numbers. This prime factorisation is nothing but the product of prime numbers.