Least Common Multiple (LCM) of 157 and 104
The least common multiple (LCM) of 157 and 104 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 157 and 104?
First, calculate the GCD of 157 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 104 = 1 remainder 53 |
| 2 | 104 ÷ 53 = 1 remainder 51 |
| 3 | 53 ÷ 51 = 1 remainder 2 |
| 4 | 51 ÷ 2 = 25 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 87 | 4872 |
| 165 and 24 | 1320 |
| 109 and 36 | 3924 |
| 115 and 171 | 19665 |
| 102 and 85 | 510 |