Question

B) Find the smallest 3 digit number exactly divisible by 4,5 and 6.​

Answer 1

Answer: 120

Step-by-step explanation:The answer is 120. The three numbers 4, 5 and 6 are all contain one or more of the prime numbers 2, 3 and5. The smallest number formed from these 3 prime numbers is 30. This product contains only 2 digits, so the 3 digit number we seek must include at least one of the prime numbers 2, 3 or 5 more than once. Furthermore 2 must be include at least twice, since the answer must be divisible by 4. But 2x2x3x5=60 is again a 2 digit number, so one of the primes must again be used as a for a second or third time. Since 2 is the smallest of these primes if it is used it yields the smallest product 120.

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Answer 2

Answer:

The smallest 3 digit number exactly divisible by 4,5, and 6 is 120.

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