Least Common Multiple (LCM) of 45 and 30
The least common multiple (LCM) of 45 and 30 is 90.
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 45 and 30?
First, calculate the GCD of 45 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 30 = 1 remainder 15 |
| 2 | 30 ÷ 15 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 133 | 17822 |
| 150 and 93 | 4650 |
| 102 and 176 | 8976 |
| 169 and 193 | 32617 |
| 69 and 183 | 4209 |