Least Common Multiple (LCM) of 45 and 69
The least common multiple (LCM) of 45 and 69 is 1035.
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 69?
First, calculate the GCD of 45 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 69 = 0 remainder 45 |
| 2 | 69 ÷ 45 = 1 remainder 24 |
| 3 | 45 ÷ 24 = 1 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 60 | 1140 |
| 138 and 86 | 5934 |
| 43 and 184 | 7912 |
| 172 and 183 | 31476 |
| 192 and 162 | 5184 |