Least Common Multiple (LCM) of 90 and 118
The least common multiple (LCM) of 90 and 118 is 5310.
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 118?
First, calculate the GCD of 90 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 118 = 0 remainder 90 |
| 2 | 118 ÷ 90 = 1 remainder 28 |
| 3 | 90 ÷ 28 = 3 remainder 6 |
| 4 | 28 ÷ 6 = 4 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 158 | 10902 |
| 161 and 179 | 28819 |
| 38 and 195 | 7410 |
| 33 and 56 | 1848 |
| 123 and 113 | 13899 |