Least Common Multiple (LCM) of 114 and 90
The least common multiple (LCM) of 114 and 90 is 1710.
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 114 and 90?
First, calculate the GCD of 114 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 90 = 1 remainder 24 |
| 2 | 90 ÷ 24 = 3 remainder 18 |
| 3 | 24 ÷ 18 = 1 remainder 6 |
| 4 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 42 | 6090 |
| 194 and 113 | 21922 |
| 32 and 147 | 4704 |
| 135 and 88 | 11880 |
| 18 and 56 | 504 |