Question

two numbers are in the ratio 2:3 their LCM 516 hcf is

Answer 1

Let the two numbers be 2n2n and 3n,3n, so their sum is 5n.5n. lcm(2n,3n)lcm(2n,3n) == 6n6n == 54,54, so n=9,n=9,and so 5n= 45     .

Answer 2

Answer:

Concept:

LCM

• When two or more numbers are given, the smallest number that is a common multiple of those numbers is called the least common multiple (LCM).

HCF

• The highest common factor (HCF) is the factor that two or more given numbers have in common.
• It is also known as the "Greatest Common Divisor" (GCD).

Given:

Ratio of two numbers $2:3$.

LCM $=516$

To Find:

We need to find the HCF of 2 numbers.

Solution:

Ratio of two numbers $=2:3$

Let the two numbers be $2x$ and $3x$.

LCM of two numbers $=2*3*x=6x$

H.C.F of $2x$ and $3x$ $=x$

⇒ $6x=516$

⇒ $x=\frac{516}{6}$

⇒ $x=86$

Therefore HCF of two numbers be $86$.

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