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LCM of 16 and 48 is the smallest number among all common multiples of 16 and 48. The first few multiples of 16 and 48 are (16, 32, 48, 64, 80, 96, . . . ) and (48, 96, 144, 192, 240, 288, 336, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 48 - by prime factorization, by division method, and by listing multiples. What is the LCM of 16 and 48?Answer: LCM of 16 and 48 is 48. Explanation: The LCM of two non-zero integers, x(16) and y(48), is the smallest positive integer m(48) that is divisible by both x(16) and y(48) without any remainder. Methods to Find LCM of 16 and 48Let's look at the different methods for finding the LCM of 16 and 48.
LCM of 16 and 48 by Division MethodTo calculate the LCM of 16 and 48 by the division method, we will divide the numbers(16, 48) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 48.
The LCM of 16 and 48 is the product of all prime numbers on the left, i.e. LCM(16, 48) by division method = 2 × 2 × 2 × 2 × 3 = 48. LCM of 16 and 48 by Listing MultiplesTo calculate the LCM of 16 and 48 by listing out the common multiples, we can follow the given below steps:
∴ The least common multiple of 16 and 48 = 48. LCM of 16 and 48 by Prime FactorizationPrime factorization of 16 and 48 is (2 × 2 × 2 × 2) = 24 and (2 × 2 × 2 × 2 × 3) = 24 × 31 respectively. LCM of 16 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 31 = 48. ☛ Also Check:
LCM of 16 and 48 Examples
Example 3: The GCD and LCM of two numbers are 16 and 48 respectively. If one number is 16, find the other number. Solution: Let the other number be m. Therefore, the other number is 48. go to slidego to slidego to slide
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The LCM of 16 and 48 is 48. To find the LCM of 16 and 48, we need to find the multiples of 16 and 48 (multiples of 16 = 16, 32, 48, 64; multiples of 48 = 48, 96, 144, 192) and choose the smallest multiple that is exactly divisible by 16 and 48, i.e., 48. Which of the following is the LCM of 16 and 48? 32, 25, 10, 48The value of LCM of 16, 48 is the smallest common multiple of 16 and 48. The number satisfying the given condition is 48. What are the Methods to Find LCM of 16 and 48?The commonly used methods to find the LCM of 16 and 48 are:
If the LCM of 48 and 16 is 48, Find its GCF.LCM(48, 16) × GCF(48, 16) = 48 × 16 Since the LCM of 48 and 16 = 48 ⇒ 48 × GCF(48, 16) = 768 Therefore, the greatest common factor (GCF) = 768/48 = 16. How to Find the LCM of 16 and 48 by Prime Factorization?To find the LCM of 16 and 48 using prime factorization, we will find the prime factors, (16 = 2 × 2 × 2 × 2) and (48 = 2 × 2 × 2 × 2 × 3). LCM of 16 and 48 is the product of prime factors raised to their respective highest exponent among the numbers 16 and 48.
The HCF and LCM of two numbers is 16 and 192 respectively If one of the numbers is 64 the other one is We know that , Product of two numbers = LCM $$\displaystyle \times $$ HCF $$ x \displaystyle \times $$ 64 = 192 $$\displaystyle \times $$ 16 $$x=\displaystyle \frac{192\times 16}{64}=48$$ Last updated - April 26, 2022 Answer: HCF = 48 and LCM = 192 Step by step solution: Contents: Given numbers = 48 and 192 To find HCF and LCM by prime factorization method, first we will find prime factors of given numbers. Prime Factorization of 48: Prime Factorization of 192: 192 = 2 × 96 = 2 × 2 × 48 = 2 × 2 × 2 × 24 = 2 × 2 × 2 × 2 × 12 = 2 × 2 × 2 × 2 × 2 × 6 = 2 × 2 × 2 × 2 × 2 × 2 × 3 HCF of 48 and 192 by prime factorization method:Common factors in above prime factors of given numbers are underlined. Common prime factors = 2, 2, 2, 2, 3 Now we have to multiply these common prime factors to obtain the HCF of given numbers. HCF = 2 × 2 × 2 × 2 × 3 ∴ HCF(48, 192) = 48 LCM of 48 and 192 by prime factorization method:Now to find the LCM we will note down how many times the each factor has occurred in above prime factors of given numbers. In above table we have also noted the maximum occurrence of the each factor in the prime factors of the given numbers. Now to obtain the LCM of given numbers we will multiply each factor maximum number of times it occurred in above table. LCM = 2 × 2 × 2 × 2 × 2 × 2 × 3 ∴ LCM(48, 192) = 192 Division Method:HCF of 48 and 192 by division method:In the above division, the last divisor is 48. Hence the HCF(GCF) of 48 and 192 = 48 ∴ HCF(48, 192) = 48 LCM of 48 and 192 by division method∴ LCM(48, 192) = 192 HCF of 48 and 192 by Listing Factors Method:To find HCF by listing factors method we will list down all the factors of the given numbers. Factors of 48: 12346812162448 Factors of 192: 12346812162432486496192 The greatest common factor in the above lists will be the HCF of the given numbers. 48 is the greatest factor which is common in the above lists. ∴ HCF(48, 192) = 48 LCM of 48 and 192 by Listing Multiples Method:To find LCM by listing multiples method we will list down the multiples of given numbers. Multiples of 48: 4896144192240288336384432480 Multiples of 192: 19238457676896011521344153617281920 The lowest common multiple in the above lists will be the LCM of the given numbers. 192 is the lowest multiple which is common in the above lists. ∴ LCM(48, 192) = 192 If the HCF of two numbers is 48 and their product is 9216, what is their LCM?Solution:If the LCM of two numbers is 192 and their product is 9216, what is their HCF?Solution:HCF and LCM of two numbers is 48 and 192 respectively. If one number is 192, what is the other number?Solution:Let other number be x. |