Least Common Multiple (LCM) of 69 and 194
The least common multiple (LCM) of 69 and 194 is 13386.
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 69 and 194?
First, calculate the GCD of 69 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 194 = 0 remainder 69 |
| 2 | 194 ÷ 69 = 2 remainder 56 |
| 3 | 69 ÷ 56 = 1 remainder 13 |
| 4 | 56 ÷ 13 = 4 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 53 | 8851 |
| 112 and 115 | 12880 |
| 139 and 121 | 16819 |
| 184 and 155 | 28520 |
| 74 and 47 | 3478 |