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The ratio of two numbers is 7 : 8 and their LCM is 280. Find the smaller number.
1. 35
2. 56
3. 80
4. 40
5. 28

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Correct Answer - Option 1 : 35

Given:

Ratio of two numbers = 7 : 8

And the LCM of two numbers = 280

Concept used:

L.C.M means The Least Common Multiple of two numbers is the “smallest non-zero common number” which is a multiple of both the numbers.

Calculation:

Let the numbers be 7k and 8k.

Then, LCM of 7k and 8k = 7 × 8 × k

⇒ 56k = 280

⇒ k = 5

So, Smaller number = 7k

⇒ 7 × 5

⇒ 35

∴ The smaller number is 35.

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