Least Common Multiple (LCM) of 10 and 61
The least common multiple (LCM) of 10 and 61 is 610.
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 10 and 61?
First, calculate the GCD of 10 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 61 = 0 remainder 10 |
| 2 | 61 ÷ 10 = 6 remainder 1 |
| 3 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 142 | 9514 |
| 123 and 67 | 8241 |
| 140 and 187 | 26180 |
| 100 and 90 | 900 |
| 189 and 196 | 5292 |