Find the least common multiple of 5, 19, and 67.
A)95
B)6,365
C)1,273
D)335

Question

Quizplus · Accepted Answer

To find the least common multiple, we need to factor each number into its prime factors:
5 = 5
19 = 19
67 = 67

Then, we take the highest power of each prime factor:
5 = 5^1
19 = 19^1
67 = 67^1

Lastly, we multiply these powers of prime factors together:
5^1 x 19^1 x 67^1 = 6,365

Therefore, the least common multiple of 5, 19, and 67 is 6,365. To find the least common multiple of three numbers, we need to find the product of the three numbers divided by their greatest common divisor. To simplify our calculation, we will use prime factorization:
5 = 5
19 = 19
67 = 67
Since none of these numbers share any common factors, their greatest common divisor is 1. Therefore, the least common multiple is simply the product of the three numbers:
5 x 19 x 67 = 6,365
Thus, the answer is B.

Find the Least Common Multiple of 5, 19, and 67