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 |
|---|---|
| 110 and 154 | 770 |
| 32 and 147 | 4704 |
| 28 and 50 | 700 |
| 42 and 75 | 1050 |
| 103 and 68 | 7004 |