FAQs on Finding Least Common Multiple (LCM): Prime Factorisation Method

Question 1

1. How do you find the prime factorization of a number?

Accepted Answer

Ans. To find the prime factorization of a number, you need to break it down into its prime factors. Start by dividing the number by the smallest prime number possible, such as 2 or 3. Continue dividing until you cannot divide any further, and write down the prime factors you used. Repeat this process for each prime factor until you have completely broken down the number into its prime factors.

Question 2

2. What is the least common multiple (LCM) of two or more numbers?

Accepted Answer

Ans. The least common multiple (LCM) of two or more numbers is the smallest multiple that is evenly divisible by each of the numbers. It is the smallest common multiple of the given numbers.

Question 3

3. How do you find the LCM using the prime factorization method?

Accepted Answer

Ans. To find the LCM using the prime factorization method, you need to find the prime factorization of each number. Then, identify the highest power of each prime factor that appears in any of the factorizations. Finally, multiply all the prime factors raised to their respective highest powers to get the LCM.

Question 4

4. Can the LCM of two numbers be less than the smaller number?

Accepted Answer

Ans. No, the LCM of two numbers cannot be less than the smaller number. The LCM must always be greater than or equal to the largest number among the given numbers. This is because the LCM is a multiple of both numbers, and a multiple cannot be smaller than the number itself.

Question 5

5. What is the relationship between LCM and GCD (Greatest Common Divisor)?

Accepted Answer

Ans. The relationship between LCM and GCD is that their product is equal to the product of the two given numbers. In other words, if a and b are two numbers, then LCM(a, b) * GCD(a, b) = a * b. This relationship is known as the fundamental theorem of arithmetic and holds true for any two positive integers.

Finding Least Common Multiple (LCM) Prime Factorisation Method Video Lecture

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