Question

A natural number, when divided by 9, 10, 12 or 15, leaves a remainder of 3 in each case. What is the smallest of all such numbers?

• A. 183
• B. 153
• C. 63
• D. 123

Answer 1

Answer:

A. 183

Given:

The number on being divided by 9, 10, 12, and 15 gives a remainder of 3 in each case.

Concept:

Take LCM of all the divisions and add the remainder so obtained (same in each case) to it.

LCM = Least Common Multiple (Least value which is exactly divisible by all the given numbers)

Calculation:

$⇒9=3\times3$

$⇒10=2\times{5}$

$⇒12=2\times{2}\times{3}$

$⇒15=3\times{5}$

LCM of (9, 10, 12 and 15) $=2\times{2}\times{3}\times{3}\times{5}=180$

∴ Required number = 180 + 3 = 183.

Shortcut Trick

Required number = LCM of (9, 10, 12 and 15) + 3 = 180 + 3 = 183.