Least Common Multiple (LCM) of 55 and 157
The least common multiple (LCM) of 55 and 157 is 8635.
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 55 and 157?
First, calculate the GCD of 55 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 157 = 0 remainder 55 |
| 2 | 157 ÷ 55 = 2 remainder 47 |
| 3 | 55 ÷ 47 = 1 remainder 8 |
| 4 | 47 ÷ 8 = 5 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 48 | 192 |
| 172 and 134 | 11524 |
| 37 and 145 | 5365 |
| 49 and 178 | 8722 |
| 25 and 68 | 1700 |