Least Common Multiple (LCM) of 90 and 154
The least common multiple (LCM) of 90 and 154 is 6930.
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 154?
First, calculate the GCD of 90 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 154 = 0 remainder 90 |
| 2 | 154 ÷ 90 = 1 remainder 64 |
| 3 | 90 ÷ 64 = 1 remainder 26 |
| 4 | 64 ÷ 26 = 2 remainder 12 |
| 5 | 26 ÷ 12 = 2 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 113 | 22487 |
| 140 and 177 | 24780 |
| 191 and 53 | 10123 |
| 74 and 176 | 6512 |
| 90 and 50 | 450 |