Least Common Multiple (LCM) of 136 and 53
The least common multiple (LCM) of 136 and 53 is 7208.
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 53?
First, calculate the GCD of 136 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 53 = 2 remainder 30 |
| 2 | 53 ÷ 30 = 1 remainder 23 |
| 3 | 30 ÷ 23 = 1 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 93 | 10509 |
| 178 and 25 | 4450 |
| 168 and 91 | 2184 |
| 18 and 24 | 72 |
| 188 and 100 | 4700 |