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21 Sep 2021, 06:15
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D
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Difficulty:
5%
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Question Stats:
89% (01:44) correct
11%
(02:07)
wrong
based on 114
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If the greatest common divisor of 51 and 288 is 3, what is the least positive common multiple of 51 and 288?
A. 2896
B. 4396
C. 4696
D. 4896
E. 4996
A. 2896
B. 4396
C. 4696
D. 4896
E. 4996
21 Sep 2021, 06:33
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Bunuel
APPROACH #1: Use the prime factorization technique for determining least common multiple
51 = (3)(17)
288 = (2)(2)(2)(2)(2)(3)(3)
LCM = (3)(2)(2)(2)(2)(2)(3)(17) = 4896
Answer: D
APPROACH #2: Use the GCD/LCM formula
--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xy
Example: x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------
When we apply the formula we get: (GCD of 51 and 288)(LCM of 51 and 288) = (51)(288)
Substitute to get: (3)(LCM of 51 and 288) = (51)(288)
Solve: (LCM of 51 and 288) = (51)(288)/(3) = 4896
Answer: D
28 Oct 2022, 08:34
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Given that GCD(51,288) = 3 and We need to find LCM(51,288)
Theory: LCM of two Numbers * GCD of two numbers = Product of the numbers
=> LCM(51,288) * GCD(51,288) = 51 * 288
=> LCM(51,288) * 3 = 3 * 17 * 288
=> LCM(51,288) = 17 * 288 = 4896
So, Answer will be D
Hope it helps!
To learn more about LCM and GCD watch the following videos
Theory: LCM of two Numbers * GCD of two numbers = Product of the numbers
=> LCM(51,288) * GCD(51,288) = 51 * 288
=> LCM(51,288) * 3 = 3 * 17 * 288
=> LCM(51,288) = 17 * 288 = 4896
So, Answer will be D
Hope it helps!
To learn more about LCM and GCD watch the following videos
