The lcm of two #s is 60. one of the #s is 20. other # is even & has only two prime factors. what is the other number?
To find the other number, we need to determine its prime factors. Since the LCM (Least Common Multiple) of two numbers is the smallest number that is divisible by both numbers, we can use the given information to find the prime factors of the other number.
We are told that the LCM of the two numbers is 60. One of the numbers is 20, which means that the other number is a multiple of 20. Therefore, the other number must have at least two prime factors: one that is common with 20, and one additional prime factor.
Since 20 has prime factorization 2^2 * 5, the other number must have the same prime factor of 2 and at least one more prime factor. Additionally, it must be even, as one of its factors is 20 (which is even).
The possible prime factors for the other number are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and so on.
Considering that the number is even and has only two prime factors, we can eliminate odd prime factors like 3, 5, 7, 11, 13, and so on.
The prime factors that are left are 2, 17, 19, 23, 29, 31, and so on.
Since the number is even and has only two prime factors, we can rule out prime numbers greater than 2. Therefore, the prime factor of the other number must be 2, and the additional prime factor must be 17, 19, 23, 29, 31, or any other prime number greater than 2.
Hence, the other number can be expressed as 2 * a prime number greater than 2, where the prime number can be 17, 19, 23, 29, 31, or any other prime number greater than 2.
Therefore, the other number can be 2 * 17 = 34, 2 * 19 = 38, 2 * 23 = 46, 2 * 29 = 58, 2 * 31 = 62, or any multiples of these numbers.
So, based on the given information, the other number can be any even number that is a multiple of 34, 38, 46, 58, 62, or any multiples of these numbers.