Least Common Multiple (LCM) of 36 and 154
The least common multiple (LCM) of 36 and 154 is 2772.
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 36 and 154?
First, calculate the GCD of 36 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 154 = 0 remainder 36 |
| 2 | 154 ÷ 36 = 4 remainder 10 |
| 3 | 36 ÷ 10 = 3 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 93 | 13578 |
| 178 and 130 | 11570 |
| 138 and 146 | 10074 |
| 92 and 111 | 10212 |
| 32 and 11 | 352 |