Least Common Multiple (LCM) of 60 and 101
The least common multiple (LCM) of 60 and 101 is 6060.
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 101?
First, calculate the GCD of 60 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 101 = 0 remainder 60 |
| 2 | 101 ÷ 60 = 1 remainder 41 |
| 3 | 60 ÷ 41 = 1 remainder 19 |
| 4 | 41 ÷ 19 = 2 remainder 3 |
| 5 | 19 ÷ 3 = 6 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 135 | 405 |
| 45 and 40 | 360 |
| 172 and 194 | 16684 |
| 122 and 146 | 8906 |
| 100 and 191 | 19100 |