Find the Smallest Number which Leaves Remainder 8 and 12 when Divided by 28 and 32 Respectively

By BYJU'S Exam Prep

Updated on: September 25th, 2023

204 is the smallest number which leaves the remainder 8 and 12 when divided by 28 and 32 respectively. To calculate this answer, we will be using the prime factorization method to find the LCM. LCM refers to the Least Common Multiple and provides a number that is divisible by two numbers in an even way.

Smallest Number with Remainder 8 and 12 when Divided by 28 and 32

To find the smallest number which leaves some remainder 8 and 12 when divided by 28 and 32 respectively, we will follow the below-mentioned steps.

The first step is to subtract the remainder 8 and 12 from the given numbers 28 and 32 –

32 -12 = 20

28-8 = 20

The difference derived by subtracting both these numbers from their remainders is 20, hence, next, we will calculate the LCM of 28 and 32.

28 = 2 × 2 × 7

32 = 2 × 2 × 2 × 2 × 2

LCM = 2 × 2 × 2 × 2 × 2 × 7 = 224

Now that we know, LCM (28, 32) is 224, we will subtract the remainder of 20 from it after which we will get,

224 – 20 = 204

Hence, the smallest number which leaves some remainder 8 and 12 when divided by 28 and 32 respectively is 204

How to Calculate LCM using Prime Factorization Method?

LCM refers to the least common multiple. It can be calculated using three types of methods which are listing, division, and prime factorization. The steps to calculate LCM using the prime factorization method are provided below.

1. The first step is to find the prime factors of the given numbers.
2. After that, write down the product of primes and match all numbers when possible.
3. Get all the common factors together.
4. Multiply these factors and the answer will be the LCM.

Summary:

Find the Smallest Number which Leaves Remainder 8 and 12 when Divided by 28 and 32 Respectively

The smallest number leaving remainder 8 and 12 when divided by 28 and 32 is 204. The answer was derived by using the prime factorization method to find the LCM of the provided numbers.

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