What is the LCM (lowest common multiple) of 14, 24 and 36? Is the answer 360?

6 Answers

Simon Templar Profile
Simon Templar answered
Multiples are easy to find, doubling will give you one, as will simply adding.
A few multiples for 14 are 28, 42, and 56.
Likewise, 24 has some obvious multiples: 48, 72, 96.

Although you could simply find all the multiples of all numbers involved and find the smallest, traditionally this is done by:
1. Reducing all numbers to primes
2. Factoring out common primes
3. Multiplying the smallest collection of primes which includes everything.

By way of example: If you had 10, 14, and 21.
10 is 2 x 5
14 is 2 x 7
21 is 3 x 7

In that list, we have 2, 3, 5, and 7.

So, we'd simply need to multiply each.
2 x 3 x 5 x 7 = 210.
So 210 would be the lowest common multiple in this example.

Sometimes, instead, you have values that have multiple prime factors.

Example: If you had 20, 28, and 21
20 is 2 x 2 x 5
28 is 2 x 2 x 7
21 is 3 x 7

In this list we have 2, 3, 5, and 7 again.
However, 20 needs two 2's.

So our list is: 2, 2, 3, 5, 7.
And we'd again, simply multiply.
2 x 2 x 3 x 5 x 7 = 420.
So 420 would be the lowest common multiple in this example.

In the question above, we have 14, 24 and 36.
14 = 2 x 7
24 = 2 x 2 x 2 x 3
36 = 2 x 2 x 3 x 3

so our list is 2, 2, 2, 3, 3, 7
And 2 x 2 x 2 x 3 x 3 x 7 = 504

Thus, 504 is the LCM for those three numbers.
Deepthi Profile
Deepthi answered
Right answer is 2184
:- 2X7X12X13=2184
Oddman Profile
Oddman answered
14 = 2*7 24 = 2^3*3
36 = 2^2*3^2 LCM = 2^3*3^2*7 = 504 The product of prime factors taken to their highest power is the LCM.

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