Least Common Multiple (LCM) of 123 and 187
The least common multiple (LCM) of 123 and 187 is 23001.
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 187?
First, calculate the GCD of 123 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 187 = 0 remainder 123 |
| 2 | 187 ÷ 123 = 1 remainder 64 |
| 3 | 123 ÷ 64 = 1 remainder 59 |
| 4 | 64 ÷ 59 = 1 remainder 5 |
| 5 | 59 ÷ 5 = 11 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 51 | 1989 |
| 84 and 73 | 6132 |
| 153 and 194 | 29682 |
| 54 and 99 | 594 |
| 96 and 87 | 2784 |