Question

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

Answer 1

The prime factorization of 14,28,36,45 is:

Factors of 14 = 2 * 7

Factors of 28 = 2 * 2 * 7

Factors of 36 = 2 * 2 * 3 * 3

Factors of 45 = 3 * 3 * 5.

LCM(14,28,36,45) = 2 * 2 * 7 * 3 * 3 * 5

= > 1260.

Therefore, the smallest number = 1260 + 3  =1263.

Hope it helps!

Answer 2

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

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