Least Common Multiple (LCM) of 53 and 136
The least common multiple (LCM) of 53 and 136 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 53 and 136?
First, calculate the GCD of 53 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 136 = 0 remainder 53 |
| 2 | 136 ÷ 53 = 2 remainder 30 |
| 3 | 53 ÷ 30 = 1 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 113 | 15368 |
| 89 and 156 | 13884 |
| 93 and 86 | 7998 |
| 162 and 198 | 1782 |
| 117 and 70 | 8190 |