Least Common Multiple (LCM) of 149 and 90
The least common multiple (LCM) of 149 and 90 is 13410.
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 149 and 90?
First, calculate the GCD of 149 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 90 = 1 remainder 59 |
| 2 | 90 ÷ 59 = 1 remainder 31 |
| 3 | 59 ÷ 31 = 1 remainder 28 |
| 4 | 31 ÷ 28 = 1 remainder 3 |
| 5 | 28 ÷ 3 = 9 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 66 | 13134 |
| 54 and 91 | 4914 |
| 25 and 165 | 825 |
| 46 and 85 | 3910 |
| 55 and 192 | 10560 |