The smallest number which when diminished by 3 is divisible by 14, 28,

1.	The smallest number which when diminished by 3 is divisible by 14, 28, 36 and 45, is?
Answer» Answer: 1263 Solution - Here, at FIRST we have to find the prime factorisation of the GIVEN numbers Prime Factors of 14 = 2 × 7 Prime Factors of 28 = 2 × 2 × 7 Prime Factors of 36 = 2 × 2 × 3 × 3 Prime Factors of 45 = 3 × 3 × 5 ∴ LCM of 14, 28, 36 & 45 = 2 × 2 × 3 × 3 × 5 × 7 = 1260 ∴ REQUIRED smallest number = 1260 + 3 = 1263 The required smallest number is 1263

The smallest number which when diminished by 3 is divisible by 14, 28, 36 and 45, is?

Answer»

Answer: 1263

Solution -

Here, at FIRST we have to find the prime factorisation of the GIVEN numbers

Prime Factors of 14 = 2 × 7

Prime Factors of 28 = 2 × 2 × 7

Prime Factors of 36 = 2 × 2 × 3 × 3

Prime Factors of 45 = 3 × 3 × 5

∴ LCM of 14, 28, 36 & 45

= 2 × 2 × 3 × 3 × 5 × 7

= 1260

∴ REQUIRED smallest number = 1260 + 3

= 1263

The required smallest number is 1263