Least Common Multiple (LCM) of 71 and 32
The least common multiple (LCM) of 71 and 32 is 2272.
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 71 and 32?
First, calculate the GCD of 71 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 32 = 2 remainder 7 |
| 2 | 32 ÷ 7 = 4 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 142 | 18034 |
| 144 and 42 | 1008 |
| 124 and 137 | 16988 |
| 102 and 90 | 1530 |
| 151 and 108 | 16308 |