Find the smallest number which when diminished by 3 is divisible by 14,28,36,45
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Step-by-step explanation: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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