Least Common Multiple (LCM) of 120 and 42
The least common multiple (LCM) of 120 and 42 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 42?
First, calculate the GCD of 120 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 42 = 2 remainder 36 |
| 2 | 42 ÷ 36 = 1 remainder 6 |
| 3 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 29 | 725 |
| 62 and 145 | 8990 |
| 57 and 66 | 1254 |
| 48 and 165 | 2640 |
| 113 and 17 | 1921 |