Least Common Multiple (LCM) of 90 and 119
The least common multiple (LCM) of 90 and 119 is 10710.
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 119?
First, calculate the GCD of 90 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 119 = 0 remainder 90 |
| 2 | 119 ÷ 90 = 1 remainder 29 |
| 3 | 90 ÷ 29 = 3 remainder 3 |
| 4 | 29 ÷ 3 = 9 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 80 | 2640 |
| 31 and 38 | 1178 |
| 107 and 58 | 6206 |
| 79 and 45 | 3555 |
| 170 and 27 | 4590 |