Least Common Multiple (LCM) of 88 and 123
The least common multiple (LCM) of 88 and 123 is 10824.
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 88 and 123?
First, calculate the GCD of 88 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 88 ÷ 123 = 0 remainder 88 |
| 2 | 123 ÷ 88 = 1 remainder 35 |
| 3 | 88 ÷ 35 = 2 remainder 18 |
| 4 | 35 ÷ 18 = 1 remainder 17 |
| 5 | 18 ÷ 17 = 1 remainder 1 |
| 6 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 45 | 180 |
| 87 and 12 | 348 |
| 170 and 59 | 10030 |
| 194 and 107 | 20758 |
| 144 and 95 | 13680 |