Least Common Multiple (LCM) of 60 and 163
The least common multiple (LCM) of 60 and 163 is 9780.
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 163?
First, calculate the GCD of 60 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 163 = 0 remainder 60 |
| 2 | 163 ÷ 60 = 2 remainder 43 |
| 3 | 60 ÷ 43 = 1 remainder 17 |
| 4 | 43 ÷ 17 = 2 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 18 | 126 |
| 178 and 150 | 13350 |
| 49 and 192 | 9408 |
| 135 and 120 | 1080 |
| 80 and 138 | 5520 |