Least Common Multiple (LCM) of 45 and 29
The least common multiple (LCM) of 45 and 29 is 1305.
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 29?
First, calculate the GCD of 45 and 29 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 29 = 1 remainder 16 |
| 2 | 29 ÷ 16 = 1 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 45 | 1305 |
| 27 and 109 | 2943 |
| 99 and 172 | 17028 |
| 10 and 93 | 930 |
| 29 and 107 | 3103 |