Least Common Multiple (LCM) of 101 and 68
The least common multiple (LCM) of 101 and 68 is 6868.
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 68?
First, calculate the GCD of 101 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 68 = 1 remainder 33 |
| 2 | 68 ÷ 33 = 2 remainder 2 |
| 3 | 33 ÷ 2 = 16 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 79 | 11534 |
| 185 and 59 | 10915 |
| 35 and 79 | 2765 |
| 199 and 105 | 20895 |
| 41 and 72 | 2952 |