Question

"Jermaine is buying Halloween candy. Chocolate bars are sold in bags of 48, caramel pieces are sold in bags of 56, licorice are sold in bags of 72, and jelly beans are sold in bags of 64. Jermaine wants to make identical candy bags using all of the candy for 7 of his friends. Jermaine thinks he has enough candy to make only 6 bags. Is Jermaine correct? Why or why not? correct? Why or why not?

A - Jermaine is correct because the least common multiple of 48, 56, 72, and 64 is 6, so he can make 6 candy bags.
B - Jermaine is incorrect because least common multiple of 48, 56, 72, and 64 is 7, so he can make 7 candy bags.
C - Jermaine is incorrect because the greatest common factor of 48, 56, 72, and 64 is 8, so he can make 8 candy bags.
D - Jermaine is correct because the greatest common factor of 48, 56, 72, and 64 is 6, so he can make 6 candy bags."

Answer 1

Jermaine is incorrect because the least common multiple of 48, 56, 72, and 64 is 1,344, not 7.

Step-by-step explanation:

Jermaine is incorrect because the least common multiple of 48, 56, 72, and 64 is 1,344, not 7. To find the least common multiple (LCM), we need to find the smallest number that is divisible by all of the given numbers. We can start by listing the multiples of each number:
Chocolate bars: 48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576, 624, ..., 1,344
Caramel pieces: 56, 112, 168, ..., 1,344
Licorice: 72, 144, ..., 1,344
Jelly beans: 64, 128, 192, 256, ..., 1,344

The LCM is 1,344, which means that Jermaine can make identical candy bags using all of the candy for 7 of his friends, not just 6. Therefore, Jermaine is incorrect in thinking that he has enough candy to make only 6 bags.