Least Common Multiple (LCM) of 120 and 168
The least common multiple (LCM) of 120 and 168 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 168?
First, calculate the GCD of 120 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 168 = 0 remainder 120 |
| 2 | 168 ÷ 120 = 1 remainder 48 |
| 3 | 120 ÷ 48 = 2 remainder 24 |
| 4 | 48 ÷ 24 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 38 | 3306 |
| 45 and 171 | 855 |
| 89 and 117 | 10413 |
| 12 and 83 | 996 |
| 168 and 46 | 3864 |