Least Common Multiple (LCM) of 43 and 76
The least common multiple (LCM) of 43 and 76 is 3268.
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 43 and 76?
First, calculate the GCD of 43 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 76 = 0 remainder 43 |
| 2 | 76 ÷ 43 = 1 remainder 33 |
| 3 | 43 ÷ 33 = 1 remainder 10 |
| 4 | 33 ÷ 10 = 3 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 77 | 1617 |
| 152 and 119 | 18088 |
| 173 and 125 | 21625 |
| 139 and 182 | 25298 |
| 143 and 53 | 7579 |