Find the lowest common multiple and highest common factor of 30 and 60.

Find 30 and 60 as products of their prime factors using factor trees: 60 = 2 x 2 x 3 x 5, 30 = 2 x 3 x 5. Use a Venn diagram to represent the prime factors of 30 and 60 with the groups 'prime factors of 30' and 'prime factors of 60'. The highest common factor (HCF) is the product of the numbers in the intersection, so the prime factors of 30 and 60: HCF = 2 x 3 x 5 = 30. The lowest common multiple (LCM) is the product of the numbers in the union, so the prime factors of 30 or 60 or both: LCM = 2 x 2 x 3 x 5 = 60.