Least Common Multiple (LCM) of 120 and 140
The least common multiple (LCM) of 120 and 140 is 840.
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 140?
First, calculate the GCD of 120 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 140 = 0 remainder 120 |
| 2 | 140 ÷ 120 = 1 remainder 20 |
| 3 | 120 ÷ 20 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 44 | 2772 |
| 12 and 100 | 300 |
| 177 and 123 | 7257 |
| 189 and 161 | 4347 |
| 129 and 117 | 5031 |