LCM of 10, 12, and 15 is the smallest number among all common multiples of 10, 12, and 15. The first few multiples of 10, 12, and 15 are (10, 20, 30, 40, 50 . . .), (12, 24, 36, 48, 60 . . .), and (15, 30, 45, 60, 75 . . .) respectively. There are 3 commonly used methods to find LCM of 10, 12, 15 - by division method, by prime factorization, and by listing multiples. Show
What is the LCM of 10, 12, and 15?Answer: LCM of 10, 12, and 15 is 60. Explanation: The LCM of three non-zero integers, a(10), b(12), and c(15), is the smallest positive integer m(60) that is divisible by a(10), b(12), and c(15) without any remainder. Methods to Find LCM of 10, 12, and 15The methods to find the LCM of 10, 12, and 15 are explained below.
LCM of 10, 12, and 15 by Prime FactorizationPrime factorization of 10, 12, and 15 is (2 × 5) = 21 × 51, (2 × 2 × 3) =
22 × 31, and (3 × 5) = 31 × 51 respectively. LCM of 10, 12, and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 51 = 60. LCM of 10, 12, and 15 by Division MethodTo calculate the LCM of 10, 12, and 15 by the division method, we will divide the numbers(10, 12, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 10, 12, and 15.
The LCM of 10, 12, and 15 is the product of all prime numbers on the left, i.e. LCM(10, 12, 15) by division method = 2 × 2 × 3 × 5 = 60. LCM of 10, 12, and 15 by Listing MultiplesTo calculate the LCM of 10, 12, 15 by listing out the common multiples, we can follow the given below steps:
∴ The least common multiple of 10, 12, and 15 = 60. ☛ Also Check:
FAQs on LCM of 10, 12, and 15What is the LCM of 10, 12, and 15?The LCM of 10, 12, and 15 is 60. To find the LCM (least common multiple) of 10, 12, and 15, we need to find the multiples of 10, 12, and 15 (multiples of 10 = 10, 20, 30, 40, 60 . . . .; multiples of 12 = 12, 24, 36, 48 . . . . 60 . . . . ; multiples of 15 = 15, 30, 45, 60 . . . .) and choose the smallest multiple that is exactly divisible by 10, 12, and 15, i.e., 60. Which of the following is the LCM of 10, 12, and 15? 18, 60, 27, 11The value of LCM of 10, 12, 15 is the smallest common multiple of 10, 12, and 15. The number satisfying the given condition is 60. What is the Relation Between GCF and LCM of 10, 12, 15?The following equation can be used to express the relation between GCF and LCM of 10, 12, 15, i.e. LCM(10, 12, 15) = [(10 × 12 × 15) × GCF(10, 12, 15)]/[GCF(10, 12) × GCF(12, 15) × GCF(10, 15)]. How to Find the LCM of 10, 12, and 15 by Prime Factorization?To find the LCM of 10, 12, and 15 using
prime factorization, we will find the prime factors, (10 = 21 × 51), (12 = 22 × 31), and (15 = 31 × 51). LCM of 10, 12, and 15 is the product of prime factors raised to their respective highest exponent
among the numbers 10, 12, and 15. |