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Let's get the factors of 60 and 80 first so we can analyze how many ways we can cut the two into equal pieces.
60 = 15x2x2
40 = 2×2×2×5
From the factors, we see that we can cut the two laces by either 2m or by 4m to get equal lengths of the pieces cut.
Check:
If we cut by 2m, then the 60m cloth will be cut into 30 pieces, while the 80m long one will be cut to 40 pieces.
If we cut by 4m, then the 60m cloth will be cut to 15 pieces, while the 80m long one will be cut to 20 pieces.