Least Common Multiple (LCM) of 187 and 120
The least common multiple (LCM) of 187 and 120 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 187 and 120?
First, calculate the GCD of 187 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 120 = 1 remainder 67 |
| 2 | 120 ÷ 67 = 1 remainder 53 |
| 3 | 67 ÷ 53 = 1 remainder 14 |
| 4 | 53 ÷ 14 = 3 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 47 | 564 |
| 50 and 58 | 1450 |
| 89 and 80 | 7120 |
| 105 and 33 | 1155 |
| 46 and 93 | 4278 |