Least Common Multiple (LCM) of 38 and 52
The least common multiple (LCM) of 38 and 52 is 988.
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 38 and 52?
First, calculate the GCD of 38 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 52 = 0 remainder 38 |
| 2 | 52 ÷ 38 = 1 remainder 14 |
| 3 | 38 ÷ 14 = 2 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 70 | 280 |
| 177 and 83 | 14691 |
| 53 and 133 | 7049 |
| 134 and 151 | 20234 |
| 37 and 44 | 1628 |