Question 14 of 19intermediate💡 UnderstandTrue / False2 marks
If a number is divisible by both 9 and 4, it must be divisible by 36.
Correct Answer
Always true. If a number is divisible by both 9 and 4, it must be divisible by LCM(9, 4) = 36.
Exercise: Always, Sometimes, or Never | Q: 6 | (Chapter: Page 10)
For More Understanding
Explanation
Since 9 and 4 are coprime (their greatest common divisor is 1), the LCM of 9 and 4 is = 36. If a number is divisible by both 9 and 4, it must contain all prime factors of both numbers in its prime factorization. Therefore, it must be divisible by 36. For example, 72 is divisible by both 9 and 4, and 72 ÷ 36 = 2.