Least Common Multiple (LCM) of 45 and 10
The least common multiple (LCM) of 45 and 10 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 10?
First, calculate the GCD of 45 and 10 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 10 = 4 remainder 5 |
| 2 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 72 | 504 |
| 105 and 104 | 10920 |
| 95 and 121 | 11495 |
| 111 and 77 | 8547 |
| 115 and 132 | 15180 |