Least Common Multiple (LCM) of 117 and 87
The least common multiple (LCM) of 117 and 87 is 3393.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 117 and 87?
First, calculate the GCD of 117 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 87 = 1 remainder 30 |
| 2 | 87 ÷ 30 = 2 remainder 27 |
| 3 | 30 ÷ 27 = 1 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 33 | 3729 |
| 45 and 58 | 2610 |
| 75 and 59 | 4425 |
| 136 and 96 | 1632 |
| 20 and 63 | 1260 |