Least Common Multiple (LCM) of 164 and 120
The least common multiple (LCM) of 164 and 120 is 4920.
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 164 and 120?
First, calculate the GCD of 164 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 120 = 1 remainder 44 |
| 2 | 120 ÷ 44 = 2 remainder 32 |
| 3 | 44 ÷ 32 = 1 remainder 12 |
| 4 | 32 ÷ 12 = 2 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 165 | 27555 |
| 108 and 126 | 756 |
| 188 and 122 | 11468 |
| 46 and 107 | 4922 |
| 10 and 72 | 360 |