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 |
|---|---|
| 128 and 166 | 10624 |
| 14 and 99 | 1386 |
| 164 and 33 | 5412 |
| 136 and 125 | 17000 |
| 35 and 159 | 5565 |