Least Common Multiple (LCM) of 56 and 147
The least common multiple (LCM) of 56 and 147 is 1176.
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 147?
First, calculate the GCD of 56 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 147 = 0 remainder 56 |
| 2 | 147 ÷ 56 = 2 remainder 35 |
| 3 | 56 ÷ 35 = 1 remainder 21 |
| 4 | 35 ÷ 21 = 1 remainder 14 |
| 5 | 21 ÷ 14 = 1 remainder 7 |
| 6 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 147 | 11172 |
| 172 and 144 | 6192 |
| 30 and 39 | 390 |
| 145 and 83 | 12035 |
| 160 and 56 | 1120 |