Least Common Multiple (LCM) of 90 and 123
The least common multiple (LCM) of 90 and 123 is 3690.
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 90 and 123?
First, calculate the GCD of 90 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 123 = 0 remainder 90 |
| 2 | 123 ÷ 90 = 1 remainder 33 |
| 3 | 90 ÷ 33 = 2 remainder 24 |
| 4 | 33 ÷ 24 = 1 remainder 9 |
| 5 | 24 ÷ 9 = 2 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 62 | 4216 |
| 134 and 116 | 7772 |
| 180 and 174 | 5220 |
| 12 and 54 | 108 |
| 77 and 96 | 7392 |