Least Common Multiple (LCM) of 51 and 90
The least common multiple (LCM) of 51 and 90 is 1530.
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 51 and 90?
First, calculate the GCD of 51 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 90 = 0 remainder 51 |
| 2 | 90 ÷ 51 = 1 remainder 39 |
| 3 | 51 ÷ 39 = 1 remainder 12 |
| 4 | 39 ÷ 12 = 3 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 126 | 2016 |
| 12 and 116 | 348 |
| 117 and 153 | 1989 |
| 39 and 11 | 429 |
| 155 and 138 | 21390 |