Least Common Multiple (LCM) of 140 and 164
The least common multiple (LCM) of 140 and 164 is 5740.
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 164?
First, calculate the GCD of 140 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 164 = 0 remainder 140 |
| 2 | 164 ÷ 140 = 1 remainder 24 |
| 3 | 140 ÷ 24 = 5 remainder 20 |
| 4 | 24 ÷ 20 = 1 remainder 4 |
| 5 | 20 ÷ 4 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 78 | 546 |
| 109 and 49 | 5341 |
| 155 and 107 | 16585 |
| 56 and 130 | 3640 |
| 153 and 70 | 10710 |