Find the LCM and GCF of 8, 12 and 50 2
The Correct Answer and Explanation is:
Correct Answers:
- LCM and GCF of 8, 12, and 50
- LCM: 600
- GCF: 2
- LCM and GCF of 10, 15, and 45
- LCM: 90
- GCF: 5
- LCM and GCF of 10, 15, 20, and 30
- LCM: 60
- GCF: 5
- Fraction Calculation
- 45+56+67−89=27071890\frac{4}{5} + \frac{5}{6} + \frac{6}{7} – \frac{8}{9} = \frac{2707}{1890} or approximately 1.43
- Simplifications
- 3(−4)−10(−4)=−12+40=283(-4) – 10(-4) = -12 + 40 = 28
- −6(1−5)+7(8)=−6(−4)+56=24+56=80-6(1 – 5) + 7(8) = -6(-4) + 56 = 24 + 56 = 80
Explanation:
The least common multiple (LCM) is the smallest number that is evenly divisible by all given numbers. To determine the LCM, factorize each number, then take the highest power of all prime factors. For example, in 8, 12, and 50, their prime factorizations are 2³, 2² × 3, and 2 × 5². The LCM is found by taking the highest powers, resulting in 23×3×52=6002^3 × 3 × 5^2 = 600.
The greatest common factor (GCF) is the largest number that divides all given numbers evenly. It is determined by finding common prime factors and taking the lowest power. In 8, 12, and 50, the common factor is 2, making the GCF 2.
For fraction calculations, a common denominator must be determined, allowing addition and subtraction of numerators. The denominators 5, 6, 7, and 9 result in a least common denominator of 1890. Converting fractions accordingly and performing operations leads to 2707/1890.
For expressions, multiplication follows distributive properties, then addition and subtraction complete simplification. Negative signs are carefully handled, ensuring correct results. The solutions are 28 and 80 respectively.
