Least Common Multiple (LCM) of 56 and 153
The least common multiple (LCM) of 56 and 153 is 8568.
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 56 and 153?
First, calculate the GCD of 56 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 153 = 0 remainder 56 |
| 2 | 153 ÷ 56 = 2 remainder 41 |
| 3 | 56 ÷ 41 = 1 remainder 15 |
| 4 | 41 ÷ 15 = 2 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 39 | 1599 |
| 99 and 144 | 1584 |
| 105 and 28 | 420 |
| 75 and 102 | 2550 |
| 161 and 45 | 7245 |