If a number is a multiple of both 5 and 7, which of the following is true?
Practice Questions
1 question
Q1
If a number is a multiple of both 5 and 7, which of the following is true?
It is a multiple of 35.
It is a multiple of 12.
It is a multiple of 10.
It is a multiple of 14.
The least common multiple of 5 and 7 is 35, so any number that is a multiple of both must also be a multiple of 35.
Questions & Step-by-step Solutions
1 item
Q
Q: If a number is a multiple of both 5 and 7, which of the following is true?
Solution: The least common multiple of 5 and 7 is 35, so any number that is a multiple of both must also be a multiple of 35.
Steps: 5
Step 1: Understand what a multiple is. A multiple of a number is the result of multiplying that number by an integer (like 1, 2, 3, etc.).
Step 2: Identify the numbers we are working with, which are 5 and 7.
Step 3: Find the least common multiple (LCM) of 5 and 7. The LCM is the smallest number that both 5 and 7 can divide into without leaving a remainder.
Step 4: Calculate the LCM of 5 and 7. Since 5 and 7 are both prime numbers, their LCM is simply their product: 5 * 7 = 35.
Step 5: Conclude that any number that is a multiple of both 5 and 7 must also be a multiple of 35, because 35 is the smallest number that both can divide.
