Least Common Multiple (LCM) of 107 and 60
The least common multiple (LCM) of 107 and 60 is 6420.
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 107 and 60?
First, calculate the GCD of 107 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 60 = 1 remainder 47 |
| 2 | 60 ÷ 47 = 1 remainder 13 |
| 3 | 47 ÷ 13 = 3 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 191 | 31706 |
| 168 and 71 | 11928 |
| 109 and 145 | 15805 |
| 51 and 30 | 510 |
| 37 and 129 | 4773 |