Least Common Multiple (LCM) of 45 and 35
The least common multiple (LCM) of 45 and 35 is 315.
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 35?
First, calculate the GCD of 45 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 35 = 1 remainder 10 |
| 2 | 35 ÷ 10 = 3 remainder 5 |
| 3 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 105 | 9660 |
| 10 and 146 | 730 |
| 25 and 12 | 300 |
| 72 and 105 | 2520 |
| 144 and 195 | 9360 |