Concept of HCF and LCM Video Lecture | Quantitative Techniques for CLAT

Ans. HCF (Highest Common Factor) is the largest number that divides two or more numbers without leaving any remainder. LCM (Least Common Multiple) is the smallest number that is divisible by two or more numbers without leaving any remainder.

Ans. To find the HCF of two numbers, you can use the prime factorization method. Find the prime factors of both numbers and identify the common prime factors. Multiply all the common prime factors together to get the HCF.

Ans. To find the LCM of two numbers, you can use either the prime factorization method or the division method. In the prime factorization method, find the prime factors of both numbers and multiply the highest power of each prime factor together to get the LCM. In the division method, divide the larger number by the HCF of the two numbers, and then multiply the quotient by the smaller number to get the LCM.

Ans. No, the HCF of two numbers cannot be greater than their LCM. The HCF is always a factor of the given numbers, whereas the LCM is always a multiple of the given numbers. Since a factor cannot be greater than its multiple, the HCF of two numbers will always be less than or equal to their LCM.

Ans. HCF and LCM are useful in various real-life situations, such as: - Planning and scheduling: LCM can be used to determine the least common multiple of time intervals, helping in scheduling events and activities. - Fraction operations: HCF is used to simplify fractions by dividing both the numerator and denominator by their common factor. - Dividing resources: LCM is used to distribute resources equally among a group by finding the smallest quantity that can be divided equally among all members. - Finding patterns: LCM can be used to find patterns in repeating events or cycles, such as the least common multiple of the days on which two events occur.