Least Common Multiple (LCM) of 74 and 57
The least common multiple (LCM) of 74 and 57 is 4218.
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 74 and 57?
First, calculate the GCD of 74 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 57 = 1 remainder 17 |
| 2 | 57 ÷ 17 = 3 remainder 6 |
| 3 | 17 ÷ 6 = 2 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 13 | 2457 |
| 177 and 193 | 34161 |
| 129 and 102 | 4386 |
| 97 and 80 | 7760 |
| 178 and 154 | 13706 |