Least Common Multiple (LCM) of 140 and 67
The least common multiple (LCM) of 140 and 67 is 9380.
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 67?
First, calculate the GCD of 140 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 67 = 2 remainder 6 |
| 2 | 67 ÷ 6 = 11 remainder 1 |
| 3 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 143 | 2145 |
| 151 and 164 | 24764 |
| 157 and 100 | 15700 |
| 197 and 193 | 38021 |
| 49 and 30 | 1470 |