Least Common Multiple (LCM) of 136 and 174
The least common multiple (LCM) of 136 and 174 is 11832.
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 174?
First, calculate the GCD of 136 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 174 = 0 remainder 136 |
| 2 | 174 ÷ 136 = 1 remainder 38 |
| 3 | 136 ÷ 38 = 3 remainder 22 |
| 4 | 38 ÷ 22 = 1 remainder 16 |
| 5 | 22 ÷ 16 = 1 remainder 6 |
| 6 | 16 ÷ 6 = 2 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 188 | 10716 |
| 147 and 67 | 9849 |
| 41 and 65 | 2665 |
| 188 and 92 | 4324 |
| 89 and 167 | 14863 |