Least Common Multiple (LCM) of 72 and 194
The least common multiple (LCM) of 72 and 194 is 6984.
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 72 and 194?
First, calculate the GCD of 72 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 194 = 0 remainder 72 |
| 2 | 194 ÷ 72 = 2 remainder 50 |
| 3 | 72 ÷ 50 = 1 remainder 22 |
| 4 | 50 ÷ 22 = 2 remainder 6 |
| 5 | 22 ÷ 6 = 3 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 34 | 1122 |
| 119 and 107 | 12733 |
| 156 and 52 | 156 |
| 92 and 153 | 14076 |
| 127 and 47 | 5969 |