
Least Common Multiple (LCM) of 84 and 143
The least common multiple (LCM) of 84 and 143 is 12012.
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 84 and 143?
First, calculate the GCD of 84 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 84 ÷ 143 = 0 remainder 84 |
2 | 143 ÷ 84 = 1 remainder 59 |
3 | 84 ÷ 59 = 1 remainder 25 |
4 | 59 ÷ 25 = 2 remainder 9 |
5 | 25 ÷ 9 = 2 remainder 7 |
6 | 9 ÷ 7 = 1 remainder 2 |
7 | 7 ÷ 2 = 3 remainder 1 |
8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
191 and 114 | 21774 |
34 and 101 | 3434 |
107 and 83 | 8881 |
152 and 106 | 8056 |
74 and 47 | 3478 |