Find the smallest number which when divided by 28 and 32, respectively, leaves a remainder, 8 and 12 respectively.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The smallest number which when divided by 28 and 32, respectively, leaves a remainder, 8 and 12 respectively, is 204. The Least Common Multiple, or LCM, is the smallest common multiple of any two or more numbers. The following techniques can be used to assess the LCM of two or more numbers:

1. A list of multiple
2. The use of prime factorization

Smallest Number divided by 28 and 32

Step 1: Find the LCM

Given,

Both 32 – 12 = 20 and 28 – 8 = 20 can be divided by the necessary numbers. The needed number will therefore be 20 less than the LCM of 28 and 32.

28’s primary components include

28 = 2 x 2 x 7

32’s prime factors are

32 = 2 x 2 x 2 x 2

LCM of 28 and 32 is

LCM (28, 32) = 2 x 2 x 2 x 2 x 7 = 224

Step 2: Locate the least number that leaves a leftover.

We must deduct 20 from the LCM of 28 and 32 in order to obtain the smallest number, which leaves 8 and 12 as remainders when divided by 28 and 32. The minimum number needed is = (224 – 20) = 204 Hence, the number is 204.

Summary:

Find the smallest number which when divided by 28 and 32, respectively, leaves a remainder, 8 and 12 respectively.

The smallest number that leaves a remainder of 8 or 12 when divided by 28 or 32, respectively, is 204. The least common multiple of two given numbers 28 and 32 helps in finding the smallest number.

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