All numbers divisible by both 24 and 14 are also divisible by which of the following?Choose 1 answer:
(Choice A)
A,
106
(Choice B)
B,
84
(Choice C)
C,
131
(Choice D)
D,
83
(Choice E)
E,
138
Answers
Answered by
15
Answer:
B 84
Step-by-step explanation:
Answered by
2
Answer:
The correct answer is option (B) 84
Step-by-step explanation:
Given numbers are 24 and 14
The prime factorization of 24 = 2×2×2×3
The prime factorization of 14 = 2×7
LCM of 24 and 14 = 2×2×2×3×7 = 168
The least common multiple of 24 and 14 is 168
The numbers divisible by both 24 and 14 will the multiples of 168
Here, from the options
106 is not divisible by 168
84 is divisible by 168
131 is not divisible by 168
83 is not divisible by 168
138 is not divisible by 168
Since 84 is divisible by 168, 84 will be divisible by all the multiples of 168.
∴84 is divisible by all the numbers which are divisible by 24 and 14
Hence the correct answer is option (B)
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