Least Common Multiple (LCM) of 140 and 61
The least common multiple (LCM) of 140 and 61 is 8540.
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 140 and 61?
First, calculate the GCD of 140 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 61 = 2 remainder 18 |
| 2 | 61 ÷ 18 = 3 remainder 7 |
| 3 | 18 ÷ 7 = 2 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 121 | 23232 |
| 199 and 106 | 21094 |
| 101 and 193 | 19493 |
| 95 and 83 | 7885 |
| 174 and 117 | 6786 |