Least Common Multiple (LCM) of 167 and 123
The least common multiple (LCM) of 167 and 123 is 20541.
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 167 and 123?
First, calculate the GCD of 167 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 123 = 1 remainder 44 |
| 2 | 123 ÷ 44 = 2 remainder 35 |
| 3 | 44 ÷ 35 = 1 remainder 9 |
| 4 | 35 ÷ 9 = 3 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 172 | 8772 |
| 194 and 135 | 26190 |
| 170 and 158 | 13430 |
| 200 and 118 | 11800 |
| 40 and 190 | 760 |