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LCM of 36 and 60 is the smallest number among all common multiples of 36 and 60. The first few multiples of 36 and 60 are (36, 72, 108, 144, 180, 216, 252, . . . ) and (60, 120, 180, 240, 300, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 60 - by prime factorization, by division method, and by listing multiples. What is the LCM of 36 and 60?Answer: LCM of 36 and 60 is 180. Explanation: The LCM of two non-zero integers, x(36) and y(60), is the smallest positive integer m(180) that is divisible by both x(36) and y(60) without any remainder. Methods to Find LCM of 36 and 60The methods to find the LCM of 36 and 60 are explained below.
LCM of 36 and 60 by Prime FactorizationPrime factorization of 36 and 60 is (2 × 2 × 3 × 3) = 22 × 32 and (2 × 2 × 3 × 5) = 22 × 31 × 51 respectively. LCM of 36 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 32 × 51 = 180. LCM of 36 and 60 by Division MethodTo calculate the LCM of 36 and 60 by the division method, we will divide the numbers(36, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 60.
The LCM of 36 and 60 is the product of all prime numbers on the left, i.e. LCM(36, 60) by division method = 2 × 2 × 3 × 3 × 5 = 180. LCM of 36 and 60 by Listing MultiplesTo calculate the LCM of 36 and 60 by listing out the common multiples, we can follow the given below steps:
∴ The least common multiple of 36 and 60 = 180. ☛ Also Check:
LCM of 36 and 60 Examples
Example 2: Find the smallest number that is divisible by 36 and 60 exactly. Solution: The smallest number that is divisible by 36 and 60 exactly is their LCM.
Therefore, the LCM of 36 and 60 is 180.
Example 3: The product of two numbers is 2160. If their GCD is 12, what is their LCM? Solution: Given: GCD = 12 product of numbers = 2160 ∵ LCM × GCD = product of numbers ⇒ LCM = Product/GCD = 2160/12 Therefore, the LCM is 180. The probable combination for the given case is LCM(36, 60) = 180. go to slidego to slidego to slide
The LCM of 36 and 60 is 180. To find the LCM of 36 and 60, we need to find the multiples of 36 and 60 (multiples of 36 = 36, 72, 108, 144 . . . . 180; multiples of 60 = 60, 120, 180, 240) and choose the smallest multiple that is exactly divisible by 36 and 60, i.e., 180. If the LCM of 60 and 36 is 180, Find its GCF.LCM(60, 36) × GCF(60, 36) = 60 × 36 Since the LCM of 60 and 36 = 180 ⇒ 180 × GCF(60, 36) = 2160 Therefore, the GCF = 2160/180 = 12. How to Find the LCM of 36 and 60 by Prime Factorization?To find the LCM of 36 and 60 using prime factorization, we will find the prime factors, (36 = 2 × 2 × 3 × 3) and (60 = 2 × 2 × 3 × 5). LCM of 36 and 60 is the product of prime factors raised to their respective highest exponent among the numbers 36 and 60. What is the Least Perfect Square Divisible by 36 and 60?The least number divisible by 36 and 60 = LCM(36, 60) What are the Methods to Find LCM of 36 and 60?The commonly used methods to find the LCM of 36 and 60 are:
TCS Company Numerical Ability LCM and HCF
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