Least Common Multiple (LCM) of 123 and 157
The least common multiple (LCM) of 123 and 157 is 19311.
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 123 and 157?
First, calculate the GCD of 123 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 157 = 0 remainder 123 |
| 2 | 157 ÷ 123 = 1 remainder 34 |
| 3 | 123 ÷ 34 = 3 remainder 21 |
| 4 | 34 ÷ 21 = 1 remainder 13 |
| 5 | 21 ÷ 13 = 1 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 140 | 6440 |
| 98 and 140 | 980 |
| 70 and 167 | 11690 |
| 46 and 103 | 4738 |
| 193 and 110 | 21230 |