Least Common Multiple (LCM) of 72 and 43
The least common multiple (LCM) of 72 and 43 is 3096.
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 72 and 43?
First, calculate the GCD of 72 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 43 = 1 remainder 29 |
| 2 | 43 ÷ 29 = 1 remainder 14 |
| 3 | 29 ÷ 14 = 2 remainder 1 |
| 4 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 178 | 9078 |
| 114 and 114 | 114 |
| 172 and 140 | 6020 |
| 160 and 198 | 15840 |
| 112 and 125 | 14000 |