Question

Find the smallest 4-digit no. Which is exactly divisible by 32,36 and 48

Answer 1

PRIME FACTORIZATION METHOD

32 = 2 x 2 x 2 x 2 x 2
36 = 2 x 2 x 3 x 3 
48 = 2 x 2 x 2 x 2 x 3

LCM OF 32 , 36 AND 48 IS

2 x 2 x 2 x 2 x 2 x 3 x 3 =288

The smallest four digit number that is divisible by 288:
288 x 4 = 1152

Since 288 is divisible by 32, 36 and 48, 1152 is also divisible by all these numbers.

Therefore, 1152 is the smallest four digit number divisible by 32, 36 and 48.

Answer 2

Answer:

32=2×2×2×2×2

36=3×3×2×2

48=3×2×2×2×2

L.C.M=2×2×2×2×2×3÷3=288

The smallest 4 digit number which is exactly divisible by 288 = 288×4

= 1153