Least Common Multiple (LCM) of 60 and 110
The least common multiple (LCM) of 60 and 110 is 660.
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 110?
First, calculate the GCD of 60 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 110 = 0 remainder 60 |
| 2 | 110 ÷ 60 = 1 remainder 50 |
| 3 | 60 ÷ 50 = 1 remainder 10 |
| 4 | 50 ÷ 10 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 97 | 19303 |
| 105 and 62 | 6510 |
| 25 and 46 | 1150 |
| 112 and 40 | 560 |
| 49 and 65 | 3185 |