If a number is a multiple of both 5 and 7, which of the following is true?
Practice Questions
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.
Questions & Step-by-Step Solutions
If a number is a multiple of both 5 and 7, which of the following is true?
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.
Multiples and Least Common Multiple (LCM) – Understanding how to find the least common multiple of two numbers and recognizing that a number that is a multiple of both must also be a multiple of their LCM.
