Least Common Multiple (LCM) of 120 and 187
The least common multiple (LCM) of 120 and 187 is 22440.
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 187?
First, calculate the GCD of 120 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 187 = 0 remainder 120 |
| 2 | 187 ÷ 120 = 1 remainder 67 |
| 3 | 120 ÷ 67 = 1 remainder 53 |
| 4 | 67 ÷ 53 = 1 remainder 14 |
| 5 | 53 ÷ 14 = 3 remainder 11 |
| 6 | 14 ÷ 11 = 1 remainder 3 |
| 7 | 11 ÷ 3 = 3 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 143 | 15015 |
| 84 and 96 | 672 |
| 15 and 36 | 180 |
| 83 and 124 | 10292 |
| 15 and 161 | 2415 |