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How do you find the HCF & LCM of 3 numbers? Video Lecture - Quant
FAQs on How do you find the HCF & LCM of 3 numbers? Video Lecture - Quant
| 1. How do you find the highest common factor (HCF) and least common multiple (LCM) of three numbers? |  |
Ans. To find the HCF and LCM of three numbers, follow these steps:
1. Identify the three numbers for which you want to find the HCF and LCM.
2. Find the prime factors of each number.
3. Determine the common prime factors among the three numbers.
4. Multiply the common prime factors to find the HCF.
5. To find the LCM, multiply all the prime factors from each number, including the non-common ones, and raise each factor to its highest power.
| 2. Can you provide an example of finding the HCF and LCM of three numbers? | |
Ans. Sure! Let's say we want to find the HCF and LCM of 12, 18, and 24.
1. Prime factors of 12: 2 * 2 * 3
2. Prime factors of 18: 2 * 3 * 3
3. Prime factors of 24: 2 * 2 * 2 * 3
4. Common prime factors: 2 and 3
5. HCF = 2 * 3 = 6
6. LCM = 2 * 2 * 2 * 3 * 3 = 72
Therefore, the HCF of 12, 18, and 24 is 6, and the LCM is 72.
| 3. Is it necessary for all three numbers to have common prime factors to find the HCF and LCM? | |
Ans. No, it is not necessary for all three numbers to have common prime factors to find the HCF and LCM. The HCF is found by multiplying the common prime factors, so if there are no common prime factors, the HCF would be 1. The LCM, on the other hand, is found by multiplying all the prime factors, including the non-common ones, raised to their highest power.
| 4. What is the significance of finding the HCF and LCM of three numbers? | |
Ans. Finding the HCF and LCM of three numbers is important in various mathematical problems and applications. The HCF helps in simplifying fractions, dividing objects into equal groups, and determining the highest common divisor. The LCM is useful in determining the time or period at which two or more events will occur simultaneously, finding the least common multiple of fractions, and solving problems involving periodic cycles.
| 5. Can the HCF of three numbers be greater than their LCM? | |
Ans. No, the HCF of three numbers cannot be greater than their LCM. The HCF represents the largest common factor/divisor among the numbers, while the LCM represents the smallest common multiple. Since the LCM has to be a multiple of all the numbers, it has to be greater than or equal to the HCF.
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