Least Common Multiple (LCM) of 157 and 173
The least common multiple (LCM) of 157 and 173 is 27161.
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 173?
First, calculate the GCD of 157 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 173 = 0 remainder 157 |
| 2 | 173 ÷ 157 = 1 remainder 16 |
| 3 | 157 ÷ 16 = 9 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 68 | 2652 |
| 105 and 120 | 840 |
| 147 and 126 | 882 |
| 68 and 68 | 68 |
| 113 and 61 | 6893 |