# Find the Smallest number which when increased by 7 is exactly divisible by 6 and 32

Discover the smallest number that meets the unique criteria: when increased by 7, it becomes divisible by both 6 and 32.

by Maivizhi A

**Updated **Mar 06, 2024

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## Find the Smallest number which when increased by 7 is exactly divisible by 6 and 32

The smallest number that, when increased by 7, is exactly divisible by both 6 and 32 is 89.

To find the smallest number that, when increased by 7, is divisible by both 6 and 32, we need to find the least common multiple (LCM) of 6 and 32, and then subtract 7 from it.

The LCM of 6 and 32 is the smallest number that is divisible by both 6 and 32.

First, let's find the prime factorization of 6 and 32:

- 6 = 2 × 3
- 32 = 2^5

To find the LCM, we take the highest power of each prime factor:

LCM(6, 32) = 2^5 × 3 = 96

Now, if we subtract 7 from 96, we get:

96 - 7 = 89

So, the smallest number that, when increased by 7, is exactly divisible by both 6 and 32 is 89.

## What is LCM and HCF?

LCM stands for "Least Common Multiple," and HCF stands for "Highest Common Factor," also known as GCD (Greatest Common Divisor).

Least Common Multiple (LCM): The least common multiple of two or more integers is the smallest positive integer that is divisible by each of the given integers without leaving a remainder. For example, the least common multiple of 4 and 6 is 12 because it's the smallest number that is divisible by both 4 and 6.

Highest Common Factor (HCF) or Greatest Common Divisor (GCD): The highest common factor or greatest common divisor of two or more integers is the largest positive integer that divides each of the given integers without leaving a remainder.

For example, the greatest common divisor of 8 and 12 is 4 because it's the largest number that divides both 8 and 12 without leaving a remainder.

LCM and HCF are fundamental concepts in number theory and are often used in various mathematical problems, especially in arithmetic and algebra. They are useful in simplifying fractions, solving equations, and finding common denominators, among other applications.

## Find the Smallest number which when increased by 7 is exactly divisible by 6 and 32 - FAQs

### 1. What is the smallest number that, when increased by 7, is divisible by both 6 and 32?

The smallest number that fits this criterion is 89.

### 2. How do you find the smallest number divisible by both 6 and 32?

First, find the LCM of 6 and 32, then subtract 7 from it.

### 3. What does LCM stand for?

LCM stands for Least Common Multiple.

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