What is the smallest 4-digit number which is divisible by 18, 24 and 3

1.	What is the smallest 4-digit number which is divisible by 18, 24 and 32?1. 11122. 11523. 14404. 1584
Answer» Correct Answer - Option 2 : 1152 Given: Given numbers are 18, 24 and 32 Concept Used: LCM (Least Common Multiple): LCM of x and y is the least common multiple of x and y which is perfectly divisible by both x and y For Example, 3 → Multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, … 4 → Multiple of 4 are 4, 8, 12, 16, 20, 24, 28, 32, … Here common are 12 and 24. But of these 12 is least ∴ LCM of 3 and 4 is 12 Calculation: LCM of 18, 24 and 32 is 288 The smallest 4-digit number is 1000 Divide the smallest 4-digit number by 288 get the remainder 136 Now, (288 - 136) = 152 Required smallest number is 1000 + 152 = 1152 ∴ The smallest 4-digit number which is divisible by 18, 24 and 32 is 1152

What is the smallest 4-digit number which is divisible by 18, 24 and 32?1. 11122. 11523. 14404. 1584

Answer» Correct Answer - Option 2 : 1152

Given:

Given numbers are 18, 24 and 32

Concept Used:

LCM (Least Common Multiple): LCM of x and y is the least common multiple of x and y which is perfectly divisible by both x and y

For Example,

3 → Multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, …

4 → Multiple of 4 are 4, 8, 12, 16, 20, 24, 28, 32, …

Here common are 12 and 24. But of these 12 is least

∴ LCM of 3 and 4 is 12

Calculation:

LCM of 18, 24 and 32 is 288

The smallest 4-digit number is 1000

Divide the smallest 4-digit number by 288 get the remainder 136

Now, (288 - 136) = 152

Required smallest number is 1000 + 152 = 1152

∴ The smallest 4-digit number which is divisible by 18, 24 and 32 is 1152

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