Question

What is the LCM of 18, 30 and 50?

Answer 1

Hint: LCM or least common multiple is the simplest method to find out the smallest common multiples lying between two or more than two numbers. Generally, the common multiple is a number which is a multiple of two or more than two numbers.

Complete step by step solution:
We have 18, 30 and 50.
We can find the LCM by using the prime factorization method.
We know that the factors of 18, that is \[ 18 = 2 \times 3 \times 3\]
The factors of 30, that is \[ 30 = 2 \times 3 \times 5\]
The factors of 50 are \[ 50 = 2 \times 5 \times 5\]
We can see that the LCM of 18, 30 and 50 is \[ 2 \times {3^2} \times {5^2}\]
Hence the LCM of 18, 30 and 50 is 450.
So, the correct answer is “450”.

Note: We know that if we have a LCM of prime numbers, then their LCM is their product itself. We also have HCF or the highest common factor. That is the largest common factor of all the given numbers is known as the Highest common factor of the number. Hence the LCM of 18, 30 and 50 is 30(from above factors).