Least Common Multiple (LCM) of 90 and 159
The least common multiple (LCM) of 90 and 159 is 4770.
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 159?
First, calculate the GCD of 90 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 159 = 0 remainder 90 |
| 2 | 159 ÷ 90 = 1 remainder 69 |
| 3 | 90 ÷ 69 = 1 remainder 21 |
| 4 | 69 ÷ 21 = 3 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 58 | 116 |
| 106 and 106 | 106 |
| 121 and 87 | 10527 |
| 87 and 127 | 11049 |
| 40 and 108 | 1080 |