Edinburgh City Council, which faces making more than £90m in savings over three years, set its revenue budget at just over £1bn for 2011/12.
It expects to save £51m in efficiency measures, including reducing layers of management and improving procurement of goods and services.
Fife Council said it would be making £33.8m of cuts to balance its books.
Some of its savings are being made by combining the role of janitors and school crossing patrol officers.
Fife Council also said it needed to reduce its workforce by 10% - 15% over the next three years. It hopes these cuts will be made by natural turnover, early retirement and voluntary redundancy.
Council leader Peter Grant said additional money would go to priority areas, including £4m for social work care packages, an extra £343,000 to deal with severe weather and £80,000 to expand the outdoor education team at Lochore Meadows.
Meanwhile Edinburgh City Council said it would protect frontline services and investment in children and the most vulnerable.
Cllr Phil Wheeler, convener for finance and resources, said: "We are facing the greatest of financial challenges head on.
"We went out to the community in the largest, most open and transparent budget engagement ever undertaken by the council.
"We listened to what people said, acted on the call to protect frontline services and vulnerable people and have delivered a balanced budget."
He added: "The savings in this budget, together with the first package in September, include £51m of efficiency measures. This equates to 75% of the total savings proposed over the next three years."
East Lothian Council set its budget on Tuesday. It said, despite a £2.09m grant cut, the 2011/2012 budget would be balanced by £5.5m from reserves.
Midlothian Council is to set its budget on Tuesday 22 February.
West Lothian Council, which was the first Scottish local authority to set its budget for the next year.
Councils generally get about 80% of their money from the Scottish government.
Setting its budget, East Lothian councillors also approved a £1m town centre regeneration project for Musselburgh, £600,000 in investment for a new 'park and ride' facility for North Berwick, and £1m in funding for a new Haddington Day Centre.
Spending on education and children's services will increase by £1.75m (1.8%) compared with 2010/11 and £300,000 in grants from the Scottish government will be used to protect teacher numbers in East Lothian schools.
About £35,000 will also be set aside for a new "area-specific" police team for Musselburgh, similar to those already operating in the Tranent and Prestonpans areas.
About £105m in capital investment is planned over the next three years on projects which include new care homes for Musselburgh and Tranent; a new library for Tranent; a new library, archive and museum in Haddington; the new Dunbar primary school; a joint project for a day centre with surgery in Gullane; North Berwick and Musselburgh museums, and new community centres for Ormiston and Dunbar.
Savings of about £2.3m are to be made in the council's staffing budget in 2011/12, through "deleting unfilled posts, the non-filling of some vacancies, better management of overtime, more efficient use of casual staff and the redesign of some services".
The council also plans to invest £10m in renewable energy projects. The extra income generated from the investments, estimated at £158,000 in 2011/12, will be used to support council services.
Paul McLennan, East Lothian Council's leader, said the aim was to avoid the need for compulsory redundancies.
He said: "In common with public service providers across the country, East Lothian Council is facing serious financial challenges in the years ahead as a result of the UK government's spending cuts.
"However, thanks to sound financial management and the careful spending decisions taken by the council, we are in a position this year to be able to cushion the blow on spending cuts and protect vital frontline services, particularly adult social care and education."