Least Common Multiple (LCM) of 140 and 84
The least common multiple (LCM) of 140 and 84 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 140 and 84?
First, calculate the GCD of 140 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 84 = 1 remainder 56 |
| 2 | 84 ÷ 56 = 1 remainder 28 |
| 3 | 56 ÷ 28 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 29 | 2088 |
| 107 and 128 | 13696 |
| 19 and 112 | 2128 |
| 68 and 160 | 2720 |
| 16 and 183 | 2928 |