Least Common Multiple (LCM) of 87 and 120
The least common multiple (LCM) of 87 and 120 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 87 and 120?
First, calculate the GCD of 87 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 87 ÷ 120 = 0 remainder 87 |
| 2 | 120 ÷ 87 = 1 remainder 33 |
| 3 | 87 ÷ 33 = 2 remainder 21 |
| 4 | 33 ÷ 21 = 1 remainder 12 |
| 5 | 21 ÷ 12 = 1 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 38 | 2090 |
| 45 and 66 | 990 |
| 125 and 115 | 2875 |
| 96 and 185 | 17760 |
| 89 and 190 | 16910 |