Question

What is the LCM of 10 and 16?

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 prime factorisation method.

Complete step-by-step answer:
Given the numbers are 10 and 16.
Now we will find the factors of 10 and 16.
Factors of 10 are \[ = 2 \times 5\]
Factors of 16 are \[ = 2 \times 2 \times 2 \times 2\]
Now the common factors are \[ = 2\]
Uncommon factors are \[ = 2 \times 2 \times 2 \times 5\]
Now the product of these common and uncommon factors will be the LCM,
\[ = 2 \times 2 \times 2 \times 2 \times 5\]
On multiplying we get,
\[ = 80\]
This is the LCM of the 10 and 16.
So, the correct answer is “80”.

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.