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Ratio and Proportion

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Question : 48 of 112

Marks: +1, -0

If two numbers are in the ratio

6 :13

and their least common multiple is 312, the sum of the numbers is

75
57
76
67

Solution:

Concept:

Represent numbers as multiples of a common factor and use LCM to find the factor.

Explanation:

Let the numbers be

6x

and

13x

, where

x

is a positive integer.

Since 6 and 13 are coprime, their LCM is

6 \times 13 = 78

.

Thus, LCM of

6x

and

13x

is

78x

.

Given LCM = 312, so

78x = 312

.

Solve:

x = 312 / 78 = 4

.

Numbers:

6 \times 4 = 24

,

13 \times 4 = 52

.

Sum:

24 + 52 = 76

.

Answer:

76

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