Chat with our AI personalities
The GCF is 3.
If the GCF of two numbers is 12 and the LCM is 24, the two numbers are 12 and 24.
Write the numbers in their prime factorisations. the GCF is the product of the common primes (each time they appear). Example: 30 and 42 2 x 3 x 5 = 30 2 x 3 x 7 = 42 Select the common factors. 2 x 3 = 6, the GCF Example: 24 and 60 24 = 2 × 2 × 2 × 3 60 = 2 × 2 × 3 × 5 GCF = 2 × 2 × 3 = 12 The prime 2 appears twice in both numbers. If you use the power format of the prime factorisation, the GCF is the product of each of the common primes to the LOWEST power across the numbers. For 24 and 60 this gives: 24 = 2³ × 3 60 = 2² × 3 × 5 → GCF = 2² × 3 = 12 As the lowest power of 2 across the numbers is 2², the lowest power of 3 across the numbers is 3 = 3¹, 5 is not common, but for completeness, 24 = 2³ × 3¹ × 5⁰ since 5⁰ = 1, so the lowest power of the prime 5 across the numbers is 5⁰: → GCF = 2² × 3¹ × 5⁰ = 4 × 3 × 1 = 12.
96=2*2*2*2*2*3 108=2*2*3*3*3 They both have two 2s and one 3 in common. For GCF, multiply all the numbers that they have in common together. 2*2*3=12. For LCM, multiply the two given numbers together and divide that by the GCF. 96*108=10368, 10368/12=864. So GCF=12 and LCM=864.
LCM = 2 x 2 x 2 x 3 x 3, GCF = 2 x 3, 24 = 2 x 2 x 2 x 3 Other number = 2 x 3 x 3 = 18