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Q: What is the LCM of 18 and 21 using prime factorization?

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It is: 144

72

It is: 32*25 = 288

18 in pime exponents is 2*32 24 in prime exponents is 23*3 LCM: 23*32 = 72

Product of two numbers a and b = LCM(a,b) x GCF(a,b)...(1)Here, product of 18 and 360 = 6480Now, we shall find GCF of 18 and 360 by using the method of prime factorization.Prime factorization of 18 = 2x3x3Prime factorization of 360 = 2x2x2x3x3x5It is clear from the prime factorization that gcf = 18Now using (1) we can find LCM:LCM(18,360) = Product of 18 and 360/GCF(18,360) = 6480/18 = 360So, LCM and GCF of 18 & 360 is 360 and 18.Also, it is important to note that 360 is divisible by 18 then GCF is 18 and LCM is 360.

18 = 2*32

3 x 5 = 15 2 x 3 x 3 = 18 2 x 3 x 3 x 5 = 90, the LCM

2 x 3 x 3 = 18 2 x 2 x 5 = 20 The GCF is 2. The LCM is 180.

2 x 3 x 3 = 18 2 x 11 = 22 2 x 3 x 3 x 11 = 198, the LCM

2 x 3 = 6 3 x 3 = 9 2 x 3 x 3 = 18, the LCM

18 = 21 x 32

18 = 21 x 32

2 x 3 x 3 = 18 3 x 3 x 5 = 45 2 x 3 x 3 x 5 = 90, the LCM

2 x 3 x 3 = 18 3 x 3 x 5 = 45 2 x 3 x 3 x 5 = 90, the LCM

The LCM of 10, 18, and 27 is 270 The prime factorization of 27 is 3 x 3 x 3 The prime factorization of 18 is 3 x 3 .....x 2 The prime factorization of 10 is .... ........,,, 2 x 5 _________________ LCM:3x 3 x 3 x 2 x 5 = 270

2 x 32 = 18

2 x 32 = 18

72

2 x 3 x 3 = 18 3 x 7 = 21 2 x 3 x 3 x 7 = 126, the LCM

2 x 2 = 42 x 3 x 3 = 18Combine the factors, eliminating duplicates.2 x 2 x 3 x 3 = 36, the LCM

2 x 3 x 3 = 183 x 7 = 21Combine the factors, eliminating duplicates.2 x 3 x 3 x 7 = 126, the LCM

The prime factorization of 18 is: 2 × 3 × 3

18 = 21 x 32

2 x 3 x 3 = 18 2 x 3 x 5 = 30 2 x 3 x 3 x 5 = 90, the LCM

2 x 32 = 18