Least Common Multiple (LCM) of 104 and 157
The least common multiple (LCM) of 104 and 157 is 16328.
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 157?
First, calculate the GCD of 104 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 157 = 0 remainder 104 |
| 2 | 157 ÷ 104 = 1 remainder 53 |
| 3 | 104 ÷ 53 = 1 remainder 51 |
| 4 | 53 ÷ 51 = 1 remainder 2 |
| 5 | 51 ÷ 2 = 25 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 40 | 2280 |
| 115 and 74 | 8510 |
| 71 and 99 | 7029 |
| 140 and 95 | 2660 |
| 188 and 76 | 3572 |