Least Common Multiple (LCM) of 53 and 74
The least common multiple (LCM) of 53 and 74 is 3922.
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 53 and 74?
First, calculate the GCD of 53 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 74 = 0 remainder 53 |
| 2 | 74 ÷ 53 = 1 remainder 21 |
| 3 | 53 ÷ 21 = 2 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 200 | 1000 |
| 83 and 135 | 11205 |
| 121 and 130 | 15730 |
| 60 and 86 | 2580 |
| 101 and 66 | 6666 |