A number is divisible by both 8 and 14. What is the least number of digits in th

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Question: A number is divisible by both 8 and 14. What is the least number of digits in the smallest number that is divisible by both? (2023)

Options:

Correct Answer: 2

Exam Year: 2023

Solution:

The LCM of 8 and 14 is 56, which is a two-digit number.

A number is divisible by both 8 and 14. What is the least number of digits in the smallest number that is divisible by both? (2023)

A number is divisible by both 8 and 14. What is the least number of digits in the smallest number that is divisible by both? (2023)

Step 1: Understand what it means for a number to be divisible by both 8 and 14. This means the number can be divided by 8 and 14 without leaving a remainder.
Step 2: Find the least common multiple (LCM) of 8 and 14. The LCM is the smallest number that both 8 and 14 can divide into evenly.
Step 3: To find the LCM, first find the prime factorization of both numbers: 8 = 2^3 and 14 = 2^1 * 7^1.
Step 4: Take the highest power of each prime number from the factorizations: For 2, the highest power is 2^3 (from 8), and for 7, it is 7^1 (from 14).
Step 5: Multiply these together to find the LCM: LCM = 2^3 * 7^1 = 8 * 7 = 56.
Step 6: Now, determine how many digits are in the number 56. It has 2 digits.
Step 7: Conclude that the least number of digits in the smallest number that is divisible by both 8 and 14 is 2.

Divisibility and LCM – Understanding how to find the least common multiple (LCM) of two numbers and its implications for divisibility.
Number of Digits – Determining the number of digits in a number based on its value.