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acegmat123
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If the least common multiple of integers x and y is 840, 03 Oct 2016, 11:03
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If there are three numbers x,y,z

Can we say that,

x*y*z=LCM*GCD^2 ??


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KarishmaB
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If the least common multiple of integers x and y is 840, 04 Oct 2016, 02:55
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acegmat123
If there are three numbers x,y,z

Can we say that,

x*y*z=LCM*GCD^2 ??


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No, not correct.
GCF is only that which is common between all three.
LCM takes into account that which is common between two numbers but not all three as well. That is counted only once in the LCM.

For example:

12, 20, 30

12 = 2*2*3
20 = 2*2*5
30 = 2*3*5

LCM = 2*2*3*5 = 60
GCF = 2
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If the least common multiple of integers x and y is 840, 04 Oct 2016, 04:53
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Thank you Karishma. Now I understood.

It works only if GCF of three numbers is equal to GCF of any two numbers.

6, 10 and 14


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If the least common multiple of integers x and y is 840, 22 Oct 2020, 03:35
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If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 56.

We know the LCM AND GCF; however, we are still not able to determine x and y. We only can determine the product of xy. Insufficient.

(2) y = 168

We know the LCM of x and y is 840. Statement 2 tells us y = 168. However, we still can't determine x.

(1&2) Product of xy = LCM of xy * GCF of xy = 840 * 56 = 2=47,040.

47,040 / 168 = 280.

x = 280. Statement 1 and 2 combined is sufficient.
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If the least common multiple of integers x and y is 840, 03 Aug 2025, 18:52
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