Question

Maria found the least common multiple of 6 and 15. Her work is shown below. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . Multiples of 15: 15, 30, 45, 60, . . . The least common multiple is 60. What is Maria’s error? ANSWERS: Maria listed some values that were not multiples.
Maria listed the factors of each number instead of multiples.
Maria should have multiplied 6 and 15 to find the least common multiple.
Maria selected a multiple that is not the least of the common multiples.

Answer 1

Question :- Maria found the least common multiple of 6 and 15. Her work is shown below. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . Multiples of 15: 15, 30, 45, 60, . . . The least common multiple is 60. What is Maria’s error ?

ANSWERS :

A) Maria listed some values that were not multiples.

B) Maria listed the factors of each number instead of multiples.

C) Maria should have multiplied 6 and 15 to find the least common multiple.

D) Maria selected a multiple that is not the least of the common multiples.

Solution :-

we know that, in order to find the least common multiple

we have to find LCM of given numbers .

so, Prime factors of 6 and 15 :-

→ 6 = 2 * 3

→ 15 = 3 * 5

→ LCM = 2 * 3 * 5 = 30 .

But maria selected The least common multiple as 60 .

and as we can see that, from his work,

• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . .
• Multiples of 15: 15, 30, 45, 60, . . .

therefore, we can conclude that, Maria selected a multiple that is not the least of the common multiples.

Hence, Option (D) is correct answer.