LCM of 120 and 756

What is the LCM of 120 and 756? - The LCM of 120 and 756 is 7560. Follow the step by step instructions on how to find the least common multiple of 120 and 756.

What is the least common multiple of 120 and 756?

How to find the lcm of 120 and 756?

To find the lcm of 120 and 756, we first need to find the multiples of 120 and 756 and then choose the least common multiple that are dividable by 120 and 756.

Multiples of 120 = 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680, 1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000, 3120, 3240, 3360, 3480, 3600, 3720, 3840, 3960, 4080, 4200, 4320, 4440, 4560, 4680, 4800, 4920, 5040, 5160, 5280, 5400, 5520, 5640, 5760, 5880, 6000, 6120, 6240, 6360, 6480, 6600, 6720, 6840, 6960, 7080, 7200, 7320, 7440, 7560
Multiples of 756 = 756, 1512, 2268, 3024, 3780, 4536, 5292, 6048, 6804, 7560

The least common multiple of 120 and 756 is 7560, because 7560 is the smallest number that is divisible by both 120 and 756.

Another method to find the least common multiple of 120 and 756 is by using the prime factorization method.
To use prime factorization, we first need to find the prime factors of 120 and 756, and then get the LCM by multiplying the prime factors that are rasied to their highest power from the two sets.

Prime factorization of 120 = 2 x 2 x 2 x 3 x 5 = 2³ x 3 x 5
Prime factorization of 756 = 2 x 2 x 3 x 3 x 3 x 7 = 2² x 3³ x 7
Prime factors to the highest power = 2³ x 3³ x 5 x 7 = 7560