Least Common Multiple (LCM) of 101 and 133
The least common multiple (LCM) of 101 and 133 is 13433.
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 133?
First, calculate the GCD of 101 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 133 = 0 remainder 101 |
| 2 | 133 ÷ 101 = 1 remainder 32 |
| 3 | 101 ÷ 32 = 3 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 81 | 13689 |
| 35 and 38 | 1330 |
| 64 and 168 | 1344 |
| 105 and 40 | 840 |
| 174 and 13 | 2262 |