Least Common Multiple (LCM) of 101 and 35
The least common multiple (LCM) of 101 and 35 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 101 and 35?
First, calculate the GCD of 101 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 35 = 2 remainder 31 |
| 2 | 35 ÷ 31 = 1 remainder 4 |
| 3 | 31 ÷ 4 = 7 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 44 | 4180 |
| 131 and 72 | 9432 |
| 34 and 74 | 1258 |
| 172 and 32 | 1376 |
| 134 and 35 | 4690 |