Least Common Multiple (LCM) of 59 and 90
The least common multiple (LCM) of 59 and 90 is 5310.
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 59 and 90?
First, calculate the GCD of 59 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 90 = 0 remainder 59 |
| 2 | 90 ÷ 59 = 1 remainder 31 |
| 3 | 59 ÷ 31 = 1 remainder 28 |
| 4 | 31 ÷ 28 = 1 remainder 3 |
| 5 | 28 ÷ 3 = 9 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 81 | 1620 |
| 105 and 83 | 8715 |
| 15 and 42 | 210 |
| 200 and 172 | 8600 |
| 117 and 36 | 468 |