Least Common Multiple (LCM) of 69 and 45
The least common multiple (LCM) of 69 and 45 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 69 and 45?
First, calculate the GCD of 69 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 45 = 1 remainder 24 |
| 2 | 45 ÷ 24 = 1 remainder 21 |
| 3 | 24 ÷ 21 = 1 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 11 | 1661 |
| 155 and 59 | 9145 |
| 138 and 87 | 4002 |
| 101 and 194 | 19594 |
| 122 and 162 | 9882 |