Least Common Multiple (LCM) of 35 and 101
The least common multiple (LCM) of 35 and 101 is 3535.
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 35 and 101?
First, calculate the GCD of 35 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 101 = 0 remainder 35 |
| 2 | 101 ÷ 35 = 2 remainder 31 |
| 3 | 35 ÷ 31 = 1 remainder 4 |
| 4 | 31 ÷ 4 = 7 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 79 | 15089 |
| 130 and 96 | 6240 |
| 27 and 36 | 108 |
| 94 and 180 | 8460 |
| 102 and 176 | 8976 |