Least Common Multiple (LCM) of 140 and 75
The least common multiple (LCM) of 140 and 75 is 2100.
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 75?
First, calculate the GCD of 140 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 75 = 1 remainder 65 |
| 2 | 75 ÷ 65 = 1 remainder 10 |
| 3 | 65 ÷ 10 = 6 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 71 | 10224 |
| 82 and 117 | 9594 |
| 185 and 166 | 30710 |
| 73 and 83 | 6059 |
| 181 and 85 | 15385 |