Least Common Multiple (LCM) of 104 and 140
The least common multiple (LCM) of 104 and 140 is 3640.
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 104 and 140?
First, calculate the GCD of 104 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 140 = 0 remainder 104 |
| 2 | 140 ÷ 104 = 1 remainder 36 |
| 3 | 104 ÷ 36 = 2 remainder 32 |
| 4 | 36 ÷ 32 = 1 remainder 4 |
| 5 | 32 ÷ 4 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 120 | 1320 |
| 60 and 107 | 6420 |
| 141 and 30 | 1410 |
| 62 and 189 | 11718 |
| 23 and 51 | 1173 |