# Lowest common multiple (lcm)

The **lowest (least) common multiple** is the smallest number that is a common multiple of two or more numbers. To calculate it, we decompose all numbers in prime factors and multiply all the prime factors (common and not common) to the maximum index.

Example: Calculate the lowest common multiple of 8, 12 and 16:

8 = 2^{3}

12= 2^{2} · 3 lcm (8, 12, 16) = 2^{4} · 3 = 48

16= 2^{4}

If you want to practise, have a game at :http://www.sheppardsoftware.com/mathgames/fractions/LeastCommonMultiple.htm

**Exercises**:

1.-Calculate the lcm of:

a) 8, 12 and 16

b) 15, 20 and 25

c) 20, 24 and 32

2.-Bus lines A and B start from the same point at 7 o'clock in the morning. The A-line buses start trips every 24 minutes; The buses on the B-line start trips every 36 minutes. Later than 7 o'clock, what time do buses from both lines start trips at the same time?

Solutions: 1.-a) 48; b) 300; c) 480; 2.- 8:12 AM

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