Least Common Multiple (LCM) of 153 and 194
The least common multiple (LCM) of 153 and 194 is 29682.
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 153 and 194?
First, calculate the GCD of 153 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 194 = 0 remainder 153 |
| 2 | 194 ÷ 153 = 1 remainder 41 |
| 3 | 153 ÷ 41 = 3 remainder 30 |
| 4 | 41 ÷ 30 = 1 remainder 11 |
| 5 | 30 ÷ 11 = 2 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 169 | 8281 |
| 171 and 103 | 17613 |
| 70 and 185 | 2590 |
| 53 and 146 | 7738 |
| 33 and 108 | 1188 |