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.
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.
