Least Common Multiple (LCM) of 90 and 99
The least common multiple (LCM) of 90 and 99 is 990.
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 99?
First, calculate the GCD of 90 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 99 = 0 remainder 90 |
| 2 | 99 ÷ 90 = 1 remainder 9 |
| 3 | 90 ÷ 9 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 110 | 11110 |
| 63 and 59 | 3717 |
| 199 and 45 | 8955 |
| 149 and 95 | 14155 |
| 152 and 157 | 23864 |