Question

LCM of two numbers is 138. But their GCD is 23. The numbers
are in a ratio 1:6. Which is the largest number amongst the two?

Answer 1

Answer:

The LCM of the numbers is =138

The GCD is =23

The ratio of the numbers is =1:6

Let the numbers be x and 6x

Then according to the question

LCM×HCF=(x)(6x)

6x²=138×23

x²=138×23/6

x²=23×23

x=23

The first number is 23and the second one is 23×6=138

The largest number amongst is 138.

Answer 2

lcm=138

gcd(hcf)=23

let the numbers be x and 6x (since the ratio is 1:6)

we know that lcm×gcd=product of two numbers

=> 138×23=x×6x

3,174=6x²

x²=3,174/6

x²=529

x=√529

x=23

6x=6×23

=138

therefore the two numbers are 23 and 138

therefore the highest number is 138