Least Common Multiple (LCM) of 90 and 97
The least common multiple (LCM) of 90 and 97 is 8730.
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 97?
First, calculate the GCD of 90 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 97 = 0 remainder 90 |
| 2 | 97 ÷ 90 = 1 remainder 7 |
| 3 | 90 ÷ 7 = 12 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 149 | 18178 |
| 143 and 150 | 21450 |
| 134 and 144 | 9648 |
| 163 and 129 | 21027 |
| 116 and 67 | 7772 |