Question

Two numbers are in the ratio 3:5. their Lcm is 600 find the sum

Answer 1

let number =3x. and 5x
LCM of 3x and 5x is 15x
given that 3x and 5x=600.
15x=600
x=600/15=40.
so sum = 3x+5x=8x
8(40)=320 so sum =320

Answer 2

Concept:

The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, commonly denoted by lcm, is the smallest positive integer divisible by both a and b in arithmetic and number theory.

Given:

Two numbers ratio given i.e. $3:5$

The Least Common Multiple is $600$

To Find:

Sum of two number

Solution:

Let the numbers be $3x$ and $5x$.

The Least Common Multiple of two numbers is $15x$

But the given Least Common Multiple of two numbers is $600$

Therefore, using the above condition.

$600=15x\\x=40$

Two numbers are as follows:

$3x=120\\5x=200$

The sum of the number is $200+120=320$

Therefore the sum of the numbers is $320$.

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