Least Common Multiple (LCM) of 120 and 142
The least common multiple (LCM) of 120 and 142 is 8520.
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 142?
First, calculate the GCD of 120 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 142 = 0 remainder 120 |
| 2 | 142 ÷ 120 = 1 remainder 22 |
| 3 | 120 ÷ 22 = 5 remainder 10 |
| 4 | 22 ÷ 10 = 2 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 87 | 174 |
| 142 and 159 | 22578 |
| 132 and 112 | 3696 |
| 58 and 190 | 5510 |
| 182 and 56 | 728 |