Least Common Multiple (LCM) of 101 and 39
The least common multiple (LCM) of 101 and 39 is 3939.
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 101 and 39?
First, calculate the GCD of 101 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 39 = 2 remainder 23 |
| 2 | 39 ÷ 23 = 1 remainder 16 |
| 3 | 23 ÷ 16 = 1 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 163 and 75 | 12225 |
| 74 and 115 | 8510 |
| 111 and 81 | 2997 |
| 90 and 125 | 2250 |
| 145 and 158 | 22910 |