Least Common Multiple (LCM) of 84 and 140
The least common multiple (LCM) of 84 and 140 is 420.
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 84 and 140?
First, calculate the GCD of 84 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 140 = 0 remainder 84 |
| 2 | 140 ÷ 84 = 1 remainder 56 |
| 3 | 84 ÷ 56 = 1 remainder 28 |
| 4 | 56 ÷ 28 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 149 | 17284 |
| 56 and 198 | 5544 |
| 38 and 63 | 2394 |
| 179 and 134 | 23986 |
| 131 and 15 | 1965 |