Least Common Multiple (LCM) of 56 and 151
The least common multiple (LCM) of 56 and 151 is 8456.
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 151?
First, calculate the GCD of 56 and 151 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 151 = 0 remainder 56 |
| 2 | 151 ÷ 56 = 2 remainder 39 |
| 3 | 56 ÷ 39 = 1 remainder 17 |
| 4 | 39 ÷ 17 = 2 remainder 5 |
| 5 | 17 ÷ 5 = 3 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 56 | 2520 |
| 132 and 70 | 4620 |
| 75 and 156 | 3900 |
| 132 and 156 | 1716 |
| 95 and 156 | 14820 |