Least Common Multiple (LCM) of 67 and 101
The least common multiple (LCM) of 67 and 101 is 6767.
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 67 and 101?
First, calculate the GCD of 67 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 101 = 0 remainder 67 |
| 2 | 101 ÷ 67 = 1 remainder 34 |
| 3 | 67 ÷ 34 = 1 remainder 33 |
| 4 | 34 ÷ 33 = 1 remainder 1 |
| 5 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 23 | 1311 |
| 115 and 55 | 1265 |
| 65 and 51 | 3315 |
| 113 and 188 | 21244 |
| 161 and 18 | 2898 |