the LCM of two numbers is 240 and their HCF is 12 and one of the number is 48 find the other number
Answers
240 × 12 / 48= 60 hope it is useful for u
Answer:
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.
HCF(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 factorization, then they are identical integers.
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