Least Common Multiple (LCM) of 90 and 101
The least common multiple (LCM) of 90 and 101 is 9090.
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 101?
First, calculate the GCD of 90 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 101 = 0 remainder 90 |
| 2 | 101 ÷ 90 = 1 remainder 11 |
| 3 | 90 ÷ 11 = 8 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 68 | 680 |
| 37 and 195 | 7215 |
| 103 and 96 | 9888 |
| 159 and 199 | 31641 |
| 118 and 94 | 5546 |