Least Common Multiple (LCM) of 140 and 77
The least common multiple (LCM) of 140 and 77 is 1540.
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 77?
First, calculate the GCD of 140 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 77 = 1 remainder 63 |
| 2 | 77 ÷ 63 = 1 remainder 14 |
| 3 | 63 ÷ 14 = 4 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 72 | 576 |
| 117 and 85 | 9945 |
| 151 and 71 | 10721 |
| 76 and 146 | 5548 |
| 82 and 33 | 2706 |