the LCM of 2 numbers are 240 and 12 .if one of the number is 60 then find the other number
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y=?x=60LCM(x,y)=240GCD(x,y)=12=?=2×2×3×5=2×2×2×2×3×5=2×2×3
Now, GCD(x,y)=12 means that the prime factors of 12 are exactly the common prime factors of x and y. And LCM(x,y)=240 means that the prime factors of 240 contains all of the prime factors of x and of y.
So, we get:
240=2×2×2×2×3common×5exclusive to x
Which just leaves 2×2 that must be exclusive to y. So:
y=2×2exclusive to y×2×2×3common=24×3=48
Ans.48
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Now, GCD(x,y)=12 means that the prime factors of 12 are exactly the common prime factors of x and y. And LCM(x,y)=240 means that the prime factors of 240 contains all of the prime factors of x and of y.
So, we get:
240=2×2×2×2×3common×5exclusive to x
Which just leaves 2×2 that must be exclusive to y. So:
y=2×2exclusive to y×2×2×3common=24×3=48
Ans.48
mark this as brainliest
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