Question

How many positive integers less than or equal to 60 are divisible by 3,4 or 5,?

Answer 1

Answer:

How many positive integers less than or equal to 60 are divisible by 3, 4, or 5?

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Let’s list them, starting with those divisible by 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60

Then let’s list those divisible by 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

Next up, let’s list those divisible by 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

After appending the lists, sorting the appended list and removing duplicates, we’re left with: 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 50, 51, 52, 54, 55, 56, 57 and 60 that matches the criteria given in the question.

Finally, let’s count the number of items in that list, and we reach 36 positive integers less than or equal to 60 that are divisible by 3, 4, or 5. (Had the question been and instead of or in the list 3, 4, or 5 it would only have been 60, as it’s the least common multiple of them all.)

Answer 2

Answer:

Only one positive integer less than or equal to 60 is divisible by 3,4 or 5.

Step-by-step explanation:

LCM of 3,4 and 5 = $3\times 4\times 5$

LCM of 3,4 and 5  $=60$

Therefore, 60 is the only positive integer less than or equal to 60 is divisible by 3,4 or 5.

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