Question

least common multiple - item 2218
aram says that the least common multiple of 4 and 6 is 24. which is true about arams statement?
options:
24 is a common multiple, but not the least common multiple.
24 is not a common multiple of 4 and 6.
24 is the least common multiple.
24 is also the greatest common factor.

Explanation:

Step1: Find multiples of 4 and 6

Multiples of 4: \(4, 8, 12, 16, 20, 24, \dots\)
Multiples of 6: \(6, 12, 18, 24, \dots\)

Step2: Identify least common multiple (LCM)

The smallest common multiple of 4 and 6 is 12, not 24. But 24 is a common multiple (since both 4 and 6 divide 24).

Step3: Evaluate options

• "24 is not a common multiple of 4 and 6": False, as \(24 \div 4 = 6\) and \(24 \div 6 = 4\).
• "24 is also the greatest common factor": GCF of 4 and 6 is 2, not 24. False.
• "24 is the least common multiple": False, LCM is 12.
• "24 is a common multiple, but not the least common multiple": True, as 24 is a common multiple but 12 is smaller.

Answer:

24 is a common multiple, but not the least common multiple.