Least Common Multiple (LCM) of 120 and 141
The least common multiple (LCM) of 120 and 141 is 5640.
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 141?
First, calculate the GCD of 120 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 141 = 0 remainder 120 |
| 2 | 141 ÷ 120 = 1 remainder 21 |
| 3 | 120 ÷ 21 = 5 remainder 15 |
| 4 | 21 ÷ 15 = 1 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 29 | 4379 |
| 109 and 108 | 11772 |
| 68 and 54 | 1836 |
| 126 and 123 | 5166 |
| 145 and 57 | 8265 |