Least Common Multiple (LCM) of 120 and 164
The least common multiple (LCM) of 120 and 164 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 120 and 164?
First, calculate the GCD of 120 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 164 = 0 remainder 120 |
| 2 | 164 ÷ 120 = 1 remainder 44 |
| 3 | 120 ÷ 44 = 2 remainder 32 |
| 4 | 44 ÷ 32 = 1 remainder 12 |
| 5 | 32 ÷ 12 = 2 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 54 | 432 |
| 50 and 39 | 1950 |
| 108 and 105 | 3780 |
| 79 and 198 | 15642 |
| 38 and 156 | 2964 |