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 |
|---|---|
| 180 and 23 | 4140 |
| 118 and 158 | 9322 |
| 157 and 10 | 1570 |
| 96 and 58 | 2784 |
| 198 and 45 | 990 |