Least Common Multiple (LCM) of 60 and 105
The least common multiple (LCM) of 60 and 105 is 420.
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 105?
First, calculate the GCD of 60 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 105 = 0 remainder 60 |
| 2 | 105 ÷ 60 = 1 remainder 45 |
| 3 | 60 ÷ 45 = 1 remainder 15 |
| 4 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 115 | 6210 |
| 114 and 46 | 2622 |
| 120 and 71 | 8520 |
| 45 and 146 | 6570 |
| 84 and 54 | 756 |