What is the difference between the LCM and the HCF of the numbers 20, 30, and…
2024
What is the difference between the LCM and the HCF of the numbers 20, 30, and 40?
Answer: B. 110 — Prime factorizations: 20 = 2^2 × 5 30 = 2 × 3 × 5 40 = 2^3 × 5 LCM: Take each prime at its highest power across the numbers: 2^3, 3^1, 5^1. So LCM = 2^3 × 3^1…
- A.
100
- B.
110
- C.
120
- D.
130
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Show answer & explanation
Correct answer: B
Prime factorizations:
20 = 2^2 × 5
30 = 2 × 3 × 5
40 = 2^3 × 5
LCM:
Take each prime at its highest power across the numbers: 2^3, 3^1, 5^1. So LCM = 2^3 × 3^1 × 5^1 = 8 × 3 × 5 = 120.
HCF:
Take primes common to all numbers at their lowest powers: 2^1 and 5^1. So HCF = 2^1 × 5^1 = 2 × 5 = 10.
Difference:
LCM − HCF = 120 − 10 = 110. Therefore, the difference between the LCM and the HCF of 20, 30 and 40 is 110.
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