Least Common Multiple (LCM) of 52 and 74
The least common multiple (LCM) of 52 and 74 is 1924.
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 52 and 74?
First, calculate the GCD of 52 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 74 = 0 remainder 52 |
| 2 | 74 ÷ 52 = 1 remainder 22 |
| 3 | 52 ÷ 22 = 2 remainder 8 |
| 4 | 22 ÷ 8 = 2 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 65 | 7995 |
| 33 and 31 | 1023 |
| 157 and 117 | 18369 |
| 134 and 22 | 1474 |
| 94 and 80 | 3760 |