Least Common Multiple (LCM) of 140 and 177
The least common multiple (LCM) of 140 and 177 is 24780.
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 177?
First, calculate the GCD of 140 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 177 = 0 remainder 140 |
| 2 | 177 ÷ 140 = 1 remainder 37 |
| 3 | 140 ÷ 37 = 3 remainder 29 |
| 4 | 37 ÷ 29 = 1 remainder 8 |
| 5 | 29 ÷ 8 = 3 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 108 | 8316 |
| 133 and 178 | 23674 |
| 36 and 103 | 3708 |
| 93 and 70 | 6510 |
| 121 and 134 | 16214 |