Least Common Multiple (LCM) of 140 and 76
The least common multiple (LCM) of 140 and 76 is 2660.
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 76?
First, calculate the GCD of 140 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 76 = 1 remainder 64 |
| 2 | 76 ÷ 64 = 1 remainder 12 |
| 3 | 64 ÷ 12 = 5 remainder 4 |
| 4 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 192 | 960 |
| 70 and 84 | 420 |
| 76 and 35 | 2660 |
| 148 and 124 | 4588 |
| 21 and 117 | 819 |