Least Common Multiple (LCM) of 45 and 71
The least common multiple (LCM) of 45 and 71 is 3195.
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 71?
First, calculate the GCD of 45 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 71 = 0 remainder 45 |
| 2 | 71 ÷ 45 = 1 remainder 26 |
| 3 | 45 ÷ 26 = 1 remainder 19 |
| 4 | 26 ÷ 19 = 1 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 166 | 11786 |
| 109 and 168 | 18312 |
| 160 and 178 | 14240 |
| 188 and 98 | 9212 |
| 196 and 76 | 3724 |