Least Common Multiple (LCM) of 60 and 164
The least common multiple (LCM) of 60 and 164 is 2460.
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 60 and 164?
First, calculate the GCD of 60 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 164 = 0 remainder 60 |
| 2 | 164 ÷ 60 = 2 remainder 44 |
| 3 | 60 ÷ 44 = 1 remainder 16 |
| 4 | 44 ÷ 16 = 2 remainder 12 |
| 5 | 16 ÷ 12 = 1 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 59 | 10620 |
| 102 and 57 | 1938 |
| 136 and 196 | 6664 |
| 18 and 38 | 342 |
| 134 and 135 | 18090 |