Question

which multiples do 3 and 5 have in common? write all the common multiples of 3 and 5. 3 5 15 30 33 35 common multiples of 3 and 5

Explanation:

Step1: Recall multiples definition

A multiple of a number is the product of that number and an integer. For 3: multiples are \(3\times1 = 3\), \(3\times2 = 6\), \(3\times3 = 9\), \(3\times4 = 12\), \(3\times5 = 15\), \(3\times6 = 18\), \(3\times7 = 21\), \(3\times8 = 24\), \(3\times9 = 27\), \(3\times10 = 30\), etc. For 5: multiples are \(5\times1 = 5\), \(5\times2 = 10\), \(5\times3 = 15\), \(5\times4 = 20\), \(5\times5 = 25\), \(5\times6 = 30\), etc.

Step2: Check each number

• 3: Only a multiple of 3, not 5 (since \(3\div5\) is not an integer).
• 5: Only a multiple of 5, not 3 (since \(5\div3\) is not an integer).
• 15: \(15\div3 = 5\) (integer) and \(15\div5 = 3\) (integer), so it's a common multiple.
• 30: \(30\div3 = 10\) (integer) and \(30\div5 = 6\) (integer), so it's a common multiple.
• 33: \(33\div5 = 6.6\) (not integer), so only multiple of 3.
• 35: \(35\div3\approx11.67\) (not integer), so only multiple of 5.

Answer:

15, 30