Least Common Multiple (LCM) of 140 and 117
The least common multiple (LCM) of 140 and 117 is 16380.
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 117?
First, calculate the GCD of 140 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 117 = 1 remainder 23 |
| 2 | 117 ÷ 23 = 5 remainder 2 |
| 3 | 23 ÷ 2 = 11 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 145 | 26680 |
| 162 and 93 | 5022 |
| 170 and 109 | 18530 |
| 120 and 155 | 3720 |
| 71 and 118 | 8378 |