Question

LCM of two numbers is 138. but their GCD is 23. the numbers are in the ratio 1 is to 6. which is the largest number among the two numbers?​

Answer 1

Let the two numbers be XX and YY.

The LCM of XX and YY is 138 and their GCD is 2323 Therefore:

X×Y=GCD×LCMX×Y=GCD×LCM

X×Y=23×138X×Y=23×138

X×Y=3,174X×Y=3,174

The ratio of the two numbers is 1:61:6. If the common factor between the two numbers is nn, then:

X=nX=n

Y=6nY=6n

Therefore:

n×6n=3,174n×6n=3,174

6n2=3,1746n2=3,174

n2=529n2=529

n=√529=23n=529=23

Therefore, the two numbers are:

X=n=23X=n=23

Y=6n=23×6=138Y=6n=23×6=138

The largest number among the two is 138.

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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.