Least Common Multiple (LCM) of 120 and 87
The least common multiple (LCM) of 120 and 87 is 3480.
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 120 and 87?
First, calculate the GCD of 120 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 87 = 1 remainder 33 |
| 2 | 87 ÷ 33 = 2 remainder 21 |
| 3 | 33 ÷ 21 = 1 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 72 | 3096 |
| 199 and 56 | 11144 |
| 83 and 199 | 16517 |
| 10 and 161 | 1610 |
| 12 and 65 | 780 |