L.C.M (Lowest Common Multiple) & G.C.F (Greatest Common Factor)

Finding Factors Finding the factors of a number can be done by sequentially dividing numbers into the product. When the factors begin to repeat you have found all factors.

Lowest Common Multiple L.C.M. 40 8 10 Take two numbers If you do the times table for each at what number do they cross 1 2 3 4 5 6 7 8 8 16 24 32 40 48 56 64 10 20 30 40 50 60 70 80 The first time they cross is at 40 So it’s the Lowest Common Multiple of these two numbers

Methods of finding L.C.M. Prime Factorization method Express each of the numbers as a product of prime factors Product of the terms containing the highest powers is taken to find the L.C.M. Example: Find the LCM of 36, 40 and 45

Methods of finding L.C.M. Common Division Method Arrange the given numbers in a row Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers which are not divisible. The product of the divisors and the undivided numbers is the required L.C.M. Find the LCM of 21, 28, 36

L.C.M. Practice Problems Find the LCM of the following : 9 , 15, 18, 20 21, 45, 63, 81 168, 392, 315, 405 48, 60, 72, 96 1071, 2601

Greatest Common Factor (G.C.F.) The greatest common factor is the largest common factor of two numbers. Factors are all of the numbers that divide into a given number equally. The greatest common factor can be found by comparing all the factors of two numbers or by finding the prime factorization of two numbers

Finding The G.C.F. Using Factors Determine the greatest common factor of two numbers by finding all the factors for the two numbers then comparing them. The largest common factor of the two numbers is their greatest common factor.

G.C.F. Using Factors The greatest common factor is of 36 and 24 is 12 Find the G.C.F. of 36 and 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36 Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24 Common Factors of 36 and 24 are: 1,2,3,4,6,12 The greatest common factor is of 36 and 24 is 12

Finding the G.C.F. Using Prime Factorization To determine the greatest common factor find the prime factorization for each number. Find all of the common prime factors of the two numbers and multiply them together. Your sum is the G.C.F.

G.C.F. Using Prime Factorization Find the G.C.F. of 36 and 24 36 24 /\ /\ 2 18 2 12 2 9 2 6 3 3 2 3 36= 2×2×3×3 24= 2×2×2×3 The G.C.F. of 36 and 24 is 2×2×3=12