Least Common Multiple (LCM) of 90 and 59
The least common multiple (LCM) of 90 and 59 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 90 and 59?
First, calculate the GCD of 90 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 59 = 1 remainder 31 |
| 2 | 59 ÷ 31 = 1 remainder 28 |
| 3 | 31 ÷ 28 = 1 remainder 3 |
| 4 | 28 ÷ 3 = 9 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 151 | 6795 |
| 155 and 56 | 8680 |
| 114 and 145 | 16530 |
| 175 and 100 | 700 |
| 22 and 125 | 2750 |