Question

what is the least number which when increased by 9 is divisible by each one of 24 32 36 and 54​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Let consider the number will be = X

According the question after increased by 9 that means the number will be =( X+9), and it is completely divisible by the following number.

∴ we have to take l.c.m. of the following numbers,

24 = 2 ×2×2×3 =2³ ×3

32= 2×2×2×2×2= 2⁵

36= 2×2×3×3 = 2² ×3²

54= 2×3×3×3 =2×3³

Now the L.C.M. will be = 2⁵ × 3³ =2×2×2×2×2×3×3×3 = 864

The number 864 is completely divisible by 24,32,36and 54.

In above we see that (X+9) is completely divisible.

Hence ( x+9) = 864

X = (864 - 9)

X=855

Ans :- 855 is the least number which when increased by 9 is divisible by each one of 24 32 36 and 54.

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