Least Common Multiple (LCM) of 136 and 178
The least common multiple (LCM) of 136 and 178 is 12104.
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 136 and 178?
First, calculate the GCD of 136 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 178 = 0 remainder 136 |
| 2 | 178 ÷ 136 = 1 remainder 42 |
| 3 | 136 ÷ 42 = 3 remainder 10 |
| 4 | 42 ÷ 10 = 4 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 100 | 1700 |
| 172 and 22 | 1892 |
| 185 and 64 | 11840 |
| 154 and 111 | 17094 |
| 41 and 13 | 533 |