the product of two digit number is 2880 their gcd is 12 cm and lcm is 240 if one number is less than 50 and other number is greater than 50,then find the other number
Answers
Step-by-step explanation:
First, I will solve the original problem. Then, I will use an example to briefly explain the primary fact used to solve the original problem.
Primary Fact: The product of any two integers is equal to the product of their LCM and GCF (or HCF).
Solution: Applying the fact above we know the missing number k is found by solving the following equation: 240 × 12 = 48 × k. No need for a calculator if you realize 48 = 4 × (4 × 3), and that 240 × 12 = (60 × 4) × (4 × 3). Now we have (60 × 4) × (4 × 3). = 4 × (4 × 3) × k → 60 = k.
Why must the Primary Fact above be true? Consider the integers 24 and 30. The GCF(24,30) = 6 and the LCM(24,30) = 120. Now let’s compare the prime factorizations of the integers, their GCF, and LCM.
24 = 2² × 3
30 = 2 × 3 × 5
The prime factors of their product are 2³ × 3² × 5.
GCF(24,30) = 6 = 2 × 3
LCM(24,30) = 120 = 2³ × 3 × 5
And likewise, the prime factors of their product are
2³ × 3² × 5. Hence if two products have identical prime factorizations, then they are identical integers.