Least Common Multiple (LCM) of 38 and 101
The least common multiple (LCM) of 38 and 101 is 3838.
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 101?
First, calculate the GCD of 38 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 101 = 0 remainder 38 |
| 2 | 101 ÷ 38 = 2 remainder 25 |
| 3 | 38 ÷ 25 = 1 remainder 13 |
| 4 | 25 ÷ 13 = 1 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 90 | 450 |
| 166 and 191 | 31706 |
| 156 and 68 | 2652 |
| 20 and 136 | 680 |
| 102 and 25 | 2550 |